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YOKOYAMA Tomoo
| Mathematics, Electronics and Informatics Division | Professor |
| Mathematics |
Performance information
■ Paper- Morse hyper-graphs of topological spaces and decompositions
Tomoo Yokoyama
Journal of Applied and Computational Topology, Volume：9, Number：1, Mar. 2025
Springer Science and Business Media LLC, Scientific journal
DOI：https://doi.org/10.1007/s41468-025-00206-y
DOI ID：10.1007/s41468-025-00206-y, ISSN：2367-1726, eISSN：2367-1734 - Topological characterizations of Hamiltonian flows on unbounded surfaces
Tomoo Yokoyama
Colloquium Mathematicum, Volume：177, Number：1-2, First page：135, Last page：160, Jan. 2025
Institute of Mathematics, Polish Academy of Sciences, Scientific journal
DOI：https://doi.org/10.4064/cm8915-1-2025
DOI ID：10.4064/cm8915-1-2025, ISSN：0010-1354, eISSN：1730-6302 - A Poincaré–Bendixson theorem for flows with arbitrarily many singular points
Tomoo Yokoyama
Studia Mathematica, Volume：278, Number：2, First page：99, Last page：172, 2024, [Reviewed]
Institute of Mathematics, Polish Academy of Sciences, Scientific journal
DOI：https://doi.org/10.4064/sm230506-9-9
DOI ID：10.4064/sm230506-9-9, ISSN：0039-3223, eISSN：1730-6337 - Topological characterizations of recurrence, Poisson stability, and isometric property of flows on surfaces
Tomoo Yokoyama
Israel Journal of Mathematics, Volume：261, Number：2, First page：951, Last page：975, Dec. 2023, [Reviewed]
Springer Science and Business Media LLC, Scientific journal
DOI：https://doi.org/10.1007/s11856-023-2601-x
DOI ID：10.1007/s11856-023-2601-x, ISSN：0021-2172, eISSN：1565-8511 - Dependency of the positive and negative long-time behaviors of flows on surfaces
Tomoo Yokoyama
Journal of Differential Equations, Volume：368, First page：376, Last page：393, Sep. 2023, [Reviewed]
Elsevier BV, Scientific journal
DOI：https://doi.org/10.1016/j.jde.2023.06.008
DOI ID：10.1016/j.jde.2023.06.008, ISSN：0022-0396 - Discrete representations of orbit structures of flows for topological data analysis
Takashi Sakajo; Tomoo Yokoyama
Discrete Mathematics, Algorithms and Applications, Sep. 2022, [Reviewed]
This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called the flow of finite type, are in one-to-one correspondence with discrete structures such as trees/graphs and sequences of letters. The flow of finite type is an extension of structurally stable Hamiltonian vector fields, which appear in many theoretical and numerical investigations of two-dimensional (2D) incompressible fluid flows. Moreover, it contains compressible 2D vector fields such as the Morse–Smale vector fields and the projection of 3D vector fields onto 2D sections. The discrete representation is not only a simple symbolic identifier for the topological structure of complex flows, but it also gives rise to a new methodology of topological data analysis for flows when applied to data brought by measurements, experiments, and numerical simulations of complex flows. As a proof of concept, we provide some applications of the representation theory to 2D compressible vector fields and a 3D vector field arising in an industrial problem.
World Scientific Pub Co Pte Ltd, Scientific journal
DOI：https://doi.org/10.1142/s1793830922501439
DOI ID：10.1142/s1793830922501439, ISSN：1793-8309, eISSN：1793-8317 - Flows with time-reversal symmetric limit sets on surfaces
Tomoo Yokoyama
Proceedings of the American Mathematical Society, Aug. 2022, [Reviewed]The Long-time behavior of orbits is one of the most fundamental properties in dynamical systems. Poincaré studied the Poisson stability, which satisfies a time-reversal symmetric condition, to capture the property of whether points return arbitrarily near the initial positions after a sufficiently long time. Birkhoff introduced and studied the concept of non-wandering points, which is one of the time-reversal symmetric conditions. Moreover, minimality and pointwise periodicity satisfy the time-reversal symmetric condition for limit sets. This paper characterizes flows with the time-reversal symmetric condition for limit sets, which refine the characterization of irrational or Denjoy flows by Athanassopoulos. Using the description, we construct flows on a sphere with Lakes of Wada attractors and with an arbitrarily large number of complementary domains, which are flow versions of such examples of spherical homeomorphisms constructed by Boroński, Činč, and Liu.
American Mathematical Society (AMS), Scientific journal
DOI：https://doi.org/10.1090/proc/16113
DOI ID：10.1090/proc/16113, ISSN：0002-9939, eISSN：1088-6826 - Optimization of Flow Distribution by Topological Description and Machine Learning in Solution Growth of SiC
Masaru Isono; Shunta Harada; Kentaro Kutsukake; Tomoo Yokoyama; Miho Tagawa; Toru Ujihara
Advanced Theory and Simulations, Volume：5, Number：9, First page：2200302, Last page：2200302, Jul. 2022, [Reviewed]
Wiley, Scientific journal
DOI：https://doi.org/10.1002/adts.202200302
DOI ID：10.1002/adts.202200302, ISSN：2513-0390, eISSN：2513-0390 - Topological characterizations of Morse-Smale flows on surfaces and generic non-Morse-Smale flows
Vladislav Kibkalo; Tomoo Yokoyama
Discrete and Continuous Dynamical Systems, Volume：42, Number：10, First page：4787, Last page：4787, 2022, [Reviewed]<p style='text-indent:20px;'>It is known that <inline-formula><tex-math id="M1">\begin{document}$ C^r $\end{document}</tex-math></inline-formula> Morse-Smale vector fields form an open dense subset in the space of vector fields on orientable closed surfaces and are structurally stable for any <inline-formula><tex-math id="M2">\begin{document}$ r \in \mathbb{Z}_{\geq 1} $\end{document}</tex-math></inline-formula>. In particular, <inline-formula><tex-math id="M3">\begin{document}$ C^r $\end{document}</tex-math></inline-formula> Morse vector fields (i.e. Morse-Smale vector fields without limit cycles) form an open dense subset in the space of <inline-formula><tex-math id="M4">\begin{document}$ C^r $\end{document}</tex-math></inline-formula> gradient vector fields on orientable closed surfaces and are structurally stable. Therefore generic time evaluations of gradient flows on orientable closed surfaces (e.g. solutions of differential equations) are described by alternating sequences of Morse flows and instantaneous non-Morse gradient flows. To illustrate the generic transitions (e.g. bifurcations of singular points, transitions via heteroclinic separatrices), we characterize and list all generic non-Morse gradient flows. To construct such characterizations, we characterize isolated singular points of gradient flows on surfaces. In fact, such a singular point is a non-trivial finitely sectored singular point without elliptic sectors. Moreover, considering Morse-Smale flows as "generic gradient flows with limit cycles", we characterize and list all generic non-Morse-Smale flows.</p>
American Institute of Mathematical Sciences (AIMS), Scientific journal
DOI：https://doi.org/10.3934/dcds.2022072
DOI ID：10.3934/dcds.2022072, ISSN：1078-0947, eISSN：1553-5231 - Refinements of topological invariants of flows
Tomoo Yokoyama
Discrete and Continuous Dynamical Systems, Volume：42, Number：5, First page：2295, Last page：2295, 2022, [Reviewed]<p style='text-indent:20px;'>We construct topological invariants, called abstract weak orbit spaces, of flows and homeomorphisms on topological spaces. In particular, the abstract weak orbit spaces of flows on topological spaces are refinements of Morse graphs of flows on compact metric spaces, Reeb graphs of Hamiltonian flows with finitely many singular points on surfaces, and the CW decompositions which consist of the unstable manifolds of singular points for Morse flows on closed manifolds. Though the CW decomposition of a Morse flow is finite, the intersection of the unstable manifold and the stable manifold of closed orbits need not consist of finitely many connected components. Therefore we study the finiteness. Moreover, we consider when the time-one map reconstructs the topology of the original flow. We show that the orbit space of a Hamiltonian flow with finitely many singular points on a compact surface is homeomorphic to the abstract weak orbit space of the time-one map by taking an arbitrarily small reparametrization and that the abstract weak orbit spaces of a Morse flow on a compact manifold and the time-one map are homeomorphic. In addition, we state examples whose Morse graphs are singletons but whose abstract weak orbit spaces are not singletons.</p>
American Institute of Mathematical Sciences (AIMS), Scientific journal
DOI：https://doi.org/10.3934/dcds.2021191
DOI ID：10.3934/dcds.2021191, ISSN：1078-0947, eISSN：1553-5231 - Topological bifurcation structure of one-parameter families of C1 unimodal maps
Atsuro Sannami; Tomoo Yokoyama
Nonlinearity, Volume：34, Number：11, First page：7991, Last page：8016, Oct. 2021, [Reviewed] - A homological approach to a mathematical definition of pulmonary fibrosis and emphysema on computed tomography
Naoya Tanabe; Shizuo Kaji; Susumu Sato; Tomoo Yokoyama; Tsuyoshi Oguma; Kiminobu Tanizawa; Tomohiro Handa; Takashi Sakajo; Toyohiro Hirai
Journal of Applied Physiology, Volume：131, Number：2, First page：601, Last page：612, Aug. 2021, [Reviewed], ［International magazine］
This study proposes a homological approach to mathematically define a three-dimensional texture feature of emphysema and fibrosis on chest computed tomography using persistent homology. The proposed definition enabled accurate segmentation with comparable quality to deep learning while offering higher interpretability than deep learning-based methods.
American Physiological Society, English, Scientific journal
DOI：https://doi.org/10.1152/japplphysiol.00150.2021
DOI ID：10.1152/japplphysiol.00150.2021, ISSN：8750-7587, eISSN：1522-1601, PubMed ID：34138650 - Complete transition diagrams of generic Hamiltonian flows with a few heteroclinic orbits
Tetsuo Yokoyama; Tomoo Yokoyama
Discrete Mathematics, Algorithms and Applications, First page：2150023, Last page：2150023, Oct. 2020, [Reviewed]
We study the transition graph of generic Hamiltonian surface flows, whose vertices are the topological equivalence classes of generic Hamiltonian surface flows and whose edges are the generic transitions. Using the transition graph, we can describe time evaluations of generic Hamiltonian surface flows (e.g., fluid phenomena) as walks on the graph. We propose a method for constructing the complete transition graph of all generic Hamiltonian flows. In fact, we construct two complete transition graphs of Hamiltonian surface flows having three and four genus elements. Moreover, we demonstrate that a lower bound on the transition distance between two Hamiltonian surface flows with any number of genus elements can be calculated by solving an integer programming problem using vector representations of Hamiltonian surface flows.
World Scientific Pub Co Pte Lt, Scientific journal
DOI：https://doi.org/10.1142/s1793830921500233
DOI ID：10.1142/s1793830921500233, ISSN：1793-8309, eISSN：1793-8317 - Existence and Non-existence of Length Averages for Foliations
中野 雄史; 横山 知郎
Communications in Mathematical Physics, Volume：372, Number：254, First page：1, Last page：17, Dec. 2019, [Reviewed]
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature. Since the pioneering work of Ghys et al., it has been known that several methods of dynamical systems theory can be adopted to study of foliations. Our aim in this paper is to investigate complexity of foliations, by generalising existence problem of time averages in dynamical systems theory to foliations: It has recently been realised that a positive Lebesgue measure set of points without time averages only appears for complicated dynamical systems, such as dynamical systems with heteroclinic connections or homoclinic tangencies. In this paper, we introduce the concept of length averages to singular foliations, and attempt to collect interesting examples with/without length averages. In particular, we demonstrate that length averages exist everywhere for any codimension one C1 orientable singular foliation without degenerate singularities on a compact surface under a mild condition on quasi-minimal sets of the foliation, which is in strong contrast to time averages of surface flows.
Springer, English, Scientific journal
DOI：https://doi.org/10.1007/s00220-019-03490-9
Scopus：https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85068156200&origin=inward
Scopus Citedby：https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85068156200&origin=inward
DOI ID：10.1007/s00220-019-03490-9, ISSN：0010-3616, eISSN：1432-0916, SCOPUS ID：85068156200 - パーシステントホモロジーとレーブグラフを用いた2 次元ハミルトンベクトル場の流線位相構造の自動抽出アルゴリズム
宇田 智紀; 横山 知郎; 坂上 貴之
Volume：29, Number：2, First page：187, Last page：224, Jun. 2019, [Reviewed]
Japanese, Scientific journal
DOI：https://doi.org/10.11540/jsiamt.29.2_187
DOI ID：10.11540/jsiamt.29.2_187, CiNii Articles ID：130007667178 - 多重連結領域上の安定非圧縮流のプリミティブな局所構造変換
横山哲郎; 横山知郎
Volume：J102-D, Number：3, First page：235, Last page：238, Mar. 2019, [Reviewed] - Properness of foliations
Tomoo Yokoyama
Topology and its Applications, Jan. 2019, [Reviewed]
English, Scientific journal - Rep-cubes: Dissection of a Cube into Nets
Dawei XU; Jinfeng HUANG; Yuta NAKANE; Tomoo YOKOYAMA; Takashi HORIYAMA; Ryuhei UEHARA
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Volume：101-A, Number：9, First page：1420, Last page：1430, Sep. 2018, [Reviewed]
English, Scientific journal
DOI：https://doi.org/10.1587/transfun.E101.A.1420
DOI ID：10.1587/transfun.E101.A.1420, DBLP ID：journals/ieicet/XuHNYHU18 - ハミルトン曲面流に対応する流れの向きを考慮した極大語の列挙アルゴリズム
横山 哲郎; 横山 知郎
Aug. 2018, [Reviewed]
Japanese, Scientific journal - Tree representations of streamline topologies of structurally stable 2D incompressible flows
T. Sakajo; T. Yokoyama
IMA Journal of Applied Mathematics, Volume：83, First page：380, Last page：411, 2018, [Reviewed]
English, Scientific journal - Algorithms Enumerating Words of Hamiltonian Surface Flow
横山哲郎; 横山知郎
Oct. 2017, [Reviewed]
Japanese, Scientific journal - A topological characterization for non-wandering surface flows
Tomoo Yokoyama
Proceedings of the American Mathematical Society, Volume：144, Number：1, First page：315, Last page：323, Sep. 2015, [Reviewed]
American Mathematical Society (AMS), Scientific journal
DOI：https://doi.org/10.1090/proc/12898
DOI ID：10.1090/proc/12898, ISSN：0002-9939, eISSN：1088-6826, Web of Science ID：WOS:000364414300028 - Transitions between streamline topologies of structurally stable Hamiltonian flows in multiply connected domains
Takashi Sakajo; Tomoo Yokoyama
PHYSICA D-NONLINEAR PHENOMENA, Volume：307, First page：22, Last page：41, Jul. 2015, [Reviewed]
We consider Hamiltonian vector fields with a dipole singularity satisfying the slip boundary condition in two-dimensional multiply connected domains. One example of such Hamiltonian vector fields is an incompressible and inviscid flow in exterior multiply connected domains with a uniform flow, whose Hamiltonian is called the stream function. Here, we are concerned with topological structures of the level sets of the Hamiltonian, which we call streamlines by analogy from incompressible fluid flows. Classification of structurally stable streamline patterns has been considered in Yokoyama and Sakajo (2013), where a procedure to assign a unique sequence of words, called the maximal word, to these patterns is proposed. Thanks to this procedure, we can identify every streamline pattern with its representing sequence of words up to topological equivalence. In the present paper, based on the theory of word representations, we propose a combinatorial method to provide a list of possible transient structurally unstable streamline patterns between two different structurally stable patterns by simply comparing their maximal word representations without specifying any Hamiltonian, Although this method cannot deal with topological streamline changes induced by bifurcations, it reveals the existence of many non-trivial global transitions in a generic sense. We also demonstrate how the present theory is applied to fluid flow problems with vortex structures. (C) 2015 Elsevier B.V. All rights reserved.
ELSEVIER SCIENCE BV, English, Scientific journal
DOI：https://doi.org/10.1016/j.physd.2015.05.013
DOI ID：10.1016/j.physd.2015.05.013, ISSN：0167-2789, eISSN：1872-8022, Web of Science ID：WOS:000359174800003 - Genericity for non-wandering surface flows
T. Yokoyama
Journal of Dynamical and Control Systems, 2015, [Reviewed]
English, Scientific journal - Relativistic helicity and link in Minkowski space-time
Z. Yoshida; Y. Kawazura; T. Yokoyama
JOURNAL OF MATHEMATICAL PHYSICS, Volume：55, Number：4, Apr. 2014, [Reviewed]
A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves. (C) 2014 AIP Publishing LLC.
AMER INST PHYSICS, English, Scientific journal
DOI：https://doi.org/10.1063/1.4872236
DOI ID：10.1063/1.4872236, ISSN：0022-2488, eISSN：1089-7658, Web of Science ID：WOS:000336084100029 - Unique encoding for streamline topologies of incompressible and inviscid flows in multiply connected domains
T. Sakajo; Y. Sawamura; T. Yokoyama
Fluid Dynamics Research, Volume：46, Number：3, First page：031411, Last page：031411, 2014, [Reviewed]
This study considers the flow of incompressible and inviscid fluid in two-dimensional multiply connected domains. For such flows, encoding algorithms to assign a unique sequence of words to any structurally stable streamline topology based on the theory presented by Yokoyama and Sakajo (2013 Proc. R. Soc. A 469 20120558) are proposed. As an application, we utilize the algorithms to characterize the evolution of an incompressible and viscid flow around a flat plate inclined to the uniform flow in terms of the change of the word representations for their instantaneous streamline topologies. © 2014 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.
Institute of Physics Publishing, English, Scientific journal
DOI：https://doi.org/10.1088/0169-5983/46/3/031411
DOI ID：10.1088/0169-5983/46/3/031411, ISSN：0169-5983, eISSN：1873-7005, SCOPUS ID：84901660669, Web of Science ID：WOS:000338839200012 - Recurrence, pointwise almost periodicity and orbit closure relation for flows and foliations
Tomoo Yokoyama
Topology and its Applications, Volume：160, Number：17, First page：2196, Last page：2206, Nov. 2013, [Reviewed]
In this paper, we obtain a characterization of the recurrence of a continuous vector field w of a closed connected surface M as follows. The following are equivalent: (1) w is pointwise recurrent. (2) w is pointwise almost periodic. (3) w is minimal or pointwise periodic. Moreover, if w is regular, then the following are equivalent: (1) w is pointwise recurrent. (2) w is minimal or the orbit space M/w is either [0, 1], or S-1. (3) R is closed (where R := {(x, y)is an element of M x M vertical bar y is an element of <(O(x))over bar>} is the orbit closure relation). On the other hand, we show that the following are equivalent for a codimension one foliation F on a compact connected manifold: (1) F is pointwise almost periodic. (2) F is minimal or compact. (3) F is R-closed. Also we show that if a foliated space on a compact metrizable space is either minimal or both compact and without infinite holonomy, then it is R-closed. (C) 2013 Elsevier B.V. All rights reserved.
Elsevier BV, English, Scientific journal
DOI：https://doi.org/10.1016/j.topol.2013.09.004
DOI ID：10.1016/j.topol.2013.09.004, ISSN：0166-8641, eISSN：1879-3207, Web of Science ID：WOS:000326953100005 - R-closed homeomorphisms on surfaces
Tomoo Yokoyama
Topology and its Applications, Volume：160, Number：14, First page：1870, Last page：1875, Sep. 2013, [Reviewed]
Let f be an R-closed homeomorphism on a connected orientable closed surface M. In this paper, we show that if M has genus more than one, then each minimal set is either a periodic orbit or an extension of a Cantor set. If M = T-2 and f is neither minimal nor periodic, then either each minimal set is a finite disjoint union of essential circloids or there is a minimal set which is an extension of a Cantor set. If M = S-2 and f is not periodic but orientation-preserving (resp. reversing), then the minimal sets of f (resp. f(2)) are exactly two fixed points and a family of circloids and S-2/(f) over tilde congruent to [0, 1]. (C) 2013 Elsevier B.V. All rights reserved.
Elsevier BV, English, Scientific journal
DOI：https://doi.org/10.1016/j.topol.2013.07.016
DOI ID：10.1016/j.topol.2013.07.016, ISSN：0166-8641, Web of Science ID：WOS:000324973100003 - On the relation between completeness and H-closedness of pospaces without infinite antichains
横山 知郎
Algebra and Discrete Mathematics, Volume：15, Number：2, First page：287, Last page：294, May 2013, [Reviewed]
Lugansk Taras Shevchenko Natl. Univ., English, Scientific journal - Word representation of streamline topologies for structurally stable vortex flows in multiply connected domains
Tomoo Yokoyama; Takashi Sakajo
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume：469, Number：2150, First page：20120558, Last page：20120558, Feb. 2013, [Reviewed]
Let us consider incompressible and inviscid flows in two-dimensional domains with multiple obstacles. The instantaneous velocity field becomes a Hamiltonian vector field defined from the stream function, and it is topologically characterized by the streamline pattern that corresponds to the contour plot of the stream function. The present paper provides us with a procedure to construct structurally stable streamline patterns generated by finitely many point vortices in the presence of the uniform flow. Starting from some basic structurally stable streamline patterns in a disc of low genus, i.e. a disc with a small number of holes, we repeat some fundamental operations that append a streamline pattern by increasing one genus to them. Owing to the inductive procedure, one can assign a sequence of operations as a representing word to each structurally stable streamline pattern. We also give the canonical expression for the word representation, which allows us to make a catalogue of all possible structurally stable streamline patterns in a combinatorial manner. As an example, we show all streamline patterns in the discs of genus 1 and 2.
The Royal Society, English, Scientific journal
DOI：https://doi.org/10.1098/rspa.2012.0558
DOI ID：10.1098/rspa.2012.0558, ISSN：1364-5021, eISSN：1471-2946, Web of Science ID：WOS:000312886500008 - Minimal sets of R-closed surface homeomorphisms
Tomoo Yokoyama
Comptes Rendus Mathematique, Volume：350, Number：23-24, First page：1051, Last page：1053, Dec. 2012, [Reviewed]
Let M be an orientable connected closed surface and f be a homeomorphism on M. Suppose that the set (E) over cap (f) := {(x, y) vertical bar y is an element of O (f) (x)} is closed. Then the suspension of f satisfies one of the following conditions: 1) the closure of each element of it is toral; 2) there is a minimal set which is not locally connected. Moreover, we show that if the set (E) over cap (f) of a homeomorphism f on a compact metrizable space is closed, then so is (E) over cap (f)k for any natural number k. 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Elsevier BV, English, Scientific journal
DOI：https://doi.org/10.1016/j.crma.2012.11.002
DOI ID：10.1016/j.crma.2012.11.002, ISSN：1631-073X, Web of Science ID：WOS:000313022900012 - Codimension one minimal foliations whose leaves have fundamental groups with the same polynomial growth
Tomoo Yokoyama
Comptes Rendus Mathematique, Volume：350, Number：5-6, First page：285, Last page：287, Mar. 2012, [Reviewed]
Elsevier BV, Scientific journal
DOI：https://doi.org/10.1016/j.crma.2012.03.008
DOI ID：10.1016/j.crma.2012.03.008, ISSN：1631-073X, Web of Science ID：WOS:000304234800013 - On some classes of spectral posets
横山 知郎
Tsukuba journal of mathematics, Volume：34, Number：2, First page：213, Last page：219, Dec. 2010, [Reviewed]
University of Tsukuba, Institute of Mathematics, English, Scientific journal
ISSN：0387-4982, CiNii Articles ID：120006309489, CiNii Books ID：AA00874643 - Fixed points of certain Anosov maps on Riemannian manifolds
TOMOO YOKOYAMA
Ergodic Theory and Dynamical Systems, Volume：30, Number：4, First page：1261, Last page：1270, Aug. 2010, [Reviewed]Abstract We present sufficient conditions for Anosov-type maps on Lie groups or Riemannian manifolds to have fixed points.
Cambridge University Press (CUP), English, Scientific journal
DOI：https://doi.org/10.1017/s0143385709000492
DOI ID：10.1017/s0143385709000492, ISSN：0143-3857, eISSN：1469-4417, Web of Science ID：WOS:000280510600016 - A Poset with Spectral Scott Topology is a Quasialgebraic Domain
Tomoo Yokoyama
Order, Volume：26, Number：4, First page：331, Last page：335, Dec. 2009, [Reviewed]
Springer Science and Business Media LLC, English, Scientific journal
DOI：https://doi.org/10.1007/s11083-009-9129-5
DOI ID：10.1007/s11083-009-9129-5, ISSN：0167-8094, eISSN：1572-9273, Web of Science ID：WOS:000271751400005 - A solution to a spectral poset problem of Lewis and Ohm
Tomoo Yokoyama
Topology and its Applications, Volume：156, Number：13, First page：2220, Last page：2223, Aug. 2009, [Reviewed]
Elsevier BV, English, Scientific journal
DOI：https://doi.org/10.1016/j.topol.2009.05.004
DOI ID：10.1016/j.topol.2009.05.004, ISSN：0166-8641, Web of Science ID：WOS:000268317800009 - A counterexample for some problem for de Groot dual iterations
Tomoo Yokoyama
Topology and its Applications, Volume：156, Number：13, First page：2224, Last page：2225, Aug. 2009, [Reviewed]
Elsevier BV, English, Scientific journal
DOI：https://doi.org/10.1016/j.topol.2009.05.005
DOI ID：10.1016/j.topol.2009.05.005, ISSN：0166-8641, Web of Science ID：WOS:000268317800010 - Codimension one minimal foliations and the higher homotopy groups of leaves
Tomoo Yokoyama
Comptes Rendus Mathematique, Volume：347, Number：11-12, First page：655, Last page：658, Jun. 2009, [Reviewed]
Elsevier BV, Scientific journal
DOI：https://doi.org/10.1016/j.crma.2009.03.017
DOI ID：10.1016/j.crma.2009.03.017, ISSN：1631-073X, Web of Science ID：WOS:000266534100016 - Codimension one minimal foliations and the fundamental groups of leaves
Tomoo Yokoyama; Takashi Tsuboi
Annales de l’institut Fourier, Volume：58, Number：2, First page：723, Last page：731, 2008, [Reviewed]
Let F be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold M. We show that if the fundamental group of each leaf of F is isomorphic to Z, then F is without holonomy. We also show that if pi(2)(M) congruent to 0 and the fundamental group of each leaf of F is isomorphic to Z(k) (k is an element of Z(>= 0)), then F is without holonomy.
Cellule MathDoc/CEDRAM, English, Scientific journal
DOI：https://doi.org/10.5802/aif.2366
DOI ID：10.5802/aif.2366, ISSN：0373-0956, eISSN：1777-5310, Web of Science ID：WOS:000256687000012
- 推しの数学
横山知郎
First page：4, Last page：4, 11 Oct. 2023 - Word Representation of Streamline Topologies for Flow Structure Analysis
Yosuke Kasai, Tomoo Yokoyama, Masahiro Kanazaki, Akira Oyama
Nagare : journal of Japan Society of Fluid Mechanics, Volume：40, Number：2, First page：107, Last page：110, Apr. 2021 - Visualization of Topology of Flow
Tomoo YOKOYAMA
Journal of the Visualization Society of Japan, Volume：41, Number：162, First page：33, Last page：34, 2021
The Visualization Society of Japan
DOI：https://doi.org/10.3154/jvs.41.162_33
DOI ID：10.3154/jvs.41.162_33, ISSN：0916-4731, eISSN：1884-037X - トポロジーと微分方程式
横山知郎
Volume：12, First page：38, Last page：44, 2020 - Applications of Topological Flow Data Analysis to Real World Issues
Tomoo Yokoyama; Takashi Sakajo; Yu Sumoto
Bulletin of the Japan Society for Industrial and Applied Mathematics, Volume：32, Number：1, First page：27, Last page：31, 2020 - 二次元多重連結領域内における構造安定な非圧縮流れの文字列表現アルゴリズム (生物流体力学における流れ構造の解析と役割)
坂上 貴之; 横山 知郎; 澤村 陽一
Volume：1900, First page：11, Last page：25, Jun. 2014
ISSN：1880-2818, CiNii Articles ID：110009814710, CiNii Books ID：AN00061013 - 28aAJ-7 Helicity of Relativistic Fluid/Plasma : Link in Minkowski Space-Time
Yoshida Z.; Kawazura Y.; Yokoyama T.
Meeting abstracts of the Physical Society of Japan, Volume：69, Number：1, First page：316, Last page：316, 05 Mar. 2014
The Physical Society of Japan (JPS)
ISSN：1342-8349, CiNii Articles ID：110009834685, CiNii Books ID：AA11439205
- Topological bifurcation structure of one-parameter families of C^1 unimodal maps
横山知郎
Mar. 2025 - A Poincaré-Bendixson theorem for flows with arbitrarily many singular points
Tomoo Yokoyama
ANZIAM 2025, Feb. 2025, [International conference]
Oral presentation - Limit behaviors of flows on surfaces
横山知郎
Oct. 2024 - Dependency of the positive and negative long-time behaviors of flows on surfaces
横山知郎
Sep. 2024 - A Poincaré-Bendixson theorem for flows with arbitrarily many singular points
Tomoo Yokoyama
Saitama Dynamics 2024, Sep. 2024, [International conference] - Classification of streamline topology of vortex flows in doubly periodic domains
Tomoo Yokoyama
ICTAM 2024, Aug. 2024, [International conference]
Oral presentation - Structural stability of “incompressible” line fields on surfaces and generic intermediate line fields
横山知郎
Jun. 2024 - Topological study of 2D flows and its application
Tomoo Yokoyama
The Grad Conjecture in Fluid Mechanics and Magnetohydrodynamics: Theory and Applications, Mar. 2024, [International conference] - Topological Data Analysis for line fields and its relative topics
Tomoo Yokoyama
Feb. 2024, [Domestic conference]
Oral presentation - On blowups of stagnation points of 2D potential flows
Applied Complex and Computational Analysis Meeting, Feb. 2024, [International conference] - On semi-decomposition
Tomoo Yokoyama
Nov. 2023, [Domestic conference] - 曲面上の流れの正方向と負方向の極限の振る舞いの依存性
Tomoo Yokoyama
Nov. 2023, [Domestic conference] - Topological Flow Data Analysis and its relative topics
Tomoo Yokoyama
Oct. 2023, [Domestic conference] - Irregular behavior in foliations (Mini-course)
Dynamics of Foliations, University of Porto, Sep. 2023, [International conference] - Existence and Non-existence of Length Averages for Foliations
Tomoo Yokoyama
Geometry and Probability 2023, Aug. 2023, [International conference] - Generic transitions for flows on surfaces with or without constraints
Tomoo Yokoyama
ICIAM 2023 Tokyo Minisymposium Topological data analysis and machine learning, Aug. 2023, [International conference] - Dependency of the positive and negative long-time behaviors of flows on surfaces
Tomoo Yokoyama
Jun. 2023, [Domestic conference] - 曲面上の流れの極限集合について
Tomoo Yokoyama
May 2023, [Domestic conference] - トポロジカルな流れの解析とその応用について
2021
Invited oral presentation
- Singularity analysis of complex functions for describing complex phenomena
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), 01 Apr. 2023 - 31 Mar. 2028
Kyoto University
Grant amount(Total)：44200000, Direct funding：34000000, Indirect funding：10200000
Grant number：23H00086 - Deepening of a unified framework for treating topological dynamical systems, decomposition theory, and topological data analysis
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Apr. 2024 - Mar. 2028
Saitama University
Grant amount(Total)：3770000, Direct funding：2900000, Indirect funding：870000
Grant number：24K06733 - New studies of foliations and dynamical systems, and their applications
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), 01 Apr. 2021 - 31 Mar. 2026
The University of Tokyo
Grant amount(Total)：12480000, Direct funding：9600000, Indirect funding：2880000
Grant number：21H00980 - Complementary study on dynamical systems and foliations using methods of partially ordered set and general topology
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), 01 Apr. 2020 - 31 Mar. 2024
Grant amount(Total)：4030000, Direct funding：3100000, Indirect funding：930000
Grant number：20K03583 - Vortex dynamics on surfaces exploring new fluid phenomena brought by geometry
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), 01 Apr. 2018 - 31 Mar. 2022
Kyoto University
Grant amount(Total)：16640000, Direct funding：12800000, Indirect funding：3840000
Grant number：18H01136 - 流れの位相的な文字化理論とその計算機上への実装
2016 - 2019