| Research (Last updated 2021/7/13) |
| Research fields My research aims at the development of the qualitative theory of flows from a topological point of view. Applying the theory, we address real issues related to fluids. In fact, we work in a continuous setting. Moreover, we deal with phenomena that can be identified with continuous/discrete vector fields. For instance, I have made contributions to the following topics: classification of flows on surfaces and their generic transitions, classification of vector fields which can be obtained from 3D vector fields by taking 2D slices. Moreover, I also work on foliation, which is a generalization of a flow. In particular, I am interested in codimension one and two cases and the case with tame transversal properties. |
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| Research interest (Topology, Dynamical systems) ・Foliations ・Codimension 1,2 dynamical systems (i.e. surface flows, surface homeomorphisms, and flows on 3-manifolds) ・Partially Cyclic Ordered Tree (COT) representations of 2D flows ・Topological flow data analysis (TFDA) ・Topological invariants of flows on topological spaces |
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| Keywords ・Codimension 1,2 foliations and dynamical systems (class space, T_0 space, almost periodicity, R-closedness, recurrence, nonwandering property, poset) ・Flows on surfaces (COT representations，structural stability, Poincare-Bendixson theorem, characterizations of limit sets) ・Generalizations of Morse graphs of flows, Reeb graphs of 2D Hamiltonian flows, and CW decompositions of Morse-Smale flows |
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