7 citations · 22 across the 34 of their papers we have counts for
34 papers
Topological vortex identification for two-dimensional turbulent flows in doubly periodic domains
Mitsuaki Kimura, Takeshi Matsumoto, Takashi Sakajo +2
The dynamics and statistical properties of two-dimensional (2D) turbulence are often investigated through numerical simulations of incompressible, viscous fluids in doubly periodic…
Combinatorial structures of the space of gradient vector fields on compact surfaces
Tomoo Yokoyama
Gradient vector fields are fundamental objects from both theoretical and practical perspectives, since various phenomena can be modeled within this framework. The ``moduli space''…
Morse hyper-graphs and abstract weak orbit spaces of semi-decompositions
Tomoo Yokoyama
We introduce topological invariants of semi-decompositions (e.g. filtrations, semi-group actions, multi-valued dynamical systems, combinatorial dynamical systems) on a topological…
Recurrence for semi-decompositions
Tomoo Yokoyama
This paper constructs a foundation to analyze semi-group actions, group actions, filtrations, and decompositions in a unified manner. In fact, though the studies of decomposition c…
Dependency of the positive and negative long-time behaviors of flows on surfaces
Tomoo Yokoyama
Long-time behavior is one of the most fundamental properties in dynamical systems. The limit behaviors of flows on surfaces are captured by the Poincaré-Bendixson theorem using the…
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…