7 citations · 22 across the 34 of their papers we have counts for
10 papers · 1 filter
Morse hyper-graphs of topological spaces and decompositions
Tomoo Yokoyama
The cell complex structure is one of the most fundamental structures in topology and combinatorics, the Morse decomposition of a dynamical system analyzes the global gradient behav…
Combinatorial structures of the space of Hamiltonian vector fields on compact surfaces
Tomoo Yokoyama
In the time evolution of fluids, the topologies of fluids can be changed by the creations and annihilations of singular points and by switching combinatorial structures of separatr…
Flows with time-reversal symmetric limit sets on surfaces
Tomoo Yokoyama
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 c…
Beyond Poincar{é} recurrence: on a topological trichotomy of orbits and on the dependence of limit sets for flows on surfaces
Tomoo Yokoyama
This paper investigates the global structure of orbits for continuous flows on surfaces. One of our main results provides a topological trichotomy of orbits of flows with finitely…
Topological characterizations of Hamiltonian flows with finitely many singular points on unbounded surfaces
Tomoo Yokoyama
Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of inte…
Relations among Hamiltonian, area-preserving, and non-wandering flows on surfaces
Tomoo Yokoyama
This paper gives a topological characterization of Hamiltonian flows with finitely many singular points on compact surfaces, using the concept of ``demi-caractéristique'' in the se…
Generalization of Poincaré recurrence theorem for flows on surfaces and characterization of minimal flows on compact surfaces
Tomoo Yokoyama
Poincaré recurrence theorem implies the density of recurrent points for volume-preserving dynamical systems on compact domains. The density of closed orbits in the non-wandering se…
Topological characterizations of Morse-Smale flows on surfaces and generic non-Morse-Smale flows
Vladislav Kibkalo, Tomoo Yokoyama
It is known that 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 $r \in \m…
A Poincaré-Bendixson theorem for flows with arbitrarily many singular points
Tomoo Yokoyama
The Poincaré-Bendixson theorem is one of the most fundamental tools to capture the limit behaviors of orbits of flows. It was generalized and applied to various phenomena in dynami…
Topological Bifurcation Structure Of One-Parameter Families Of Unimodal Maps
Atsuro Sannami, Tomoo Yokoyama
We consider the bifurcation structure of one-parameter families of unimodal maps whose differentiability is only . The structure of its bifurcation diagram can be a very wild…