23 citations · 23 across the 8 of their papers we have counts for
9 papers
Multi-parameter persistence in dynamical systems for maximizing effects of control inputs
Yusuke Imoto, Tomoo Yokoyama
We introduce a new topological method to naturally extend a partial function on a ``generalization'' of a metric space equipped w…
On Discrete Morse-Bott Theory
Yuto Nishikawa, Tomoo Yokoyama
This paper shows that discrete Morse-Bott theory can be developed as a natural extension of R. Forman's discrete Morse theory by improving the definition of the discrete Morse-Bott…
Coarse non-wandering sets and their filtration
Tomoo Yokoyama
This paper investigates recurrence properties of dynamical systems under the restriction that control is available only through inputs and outputs. We introduce the concept of ``co…
Structural stability and generic transitions of "incompressible" line fields on surfaces
Tomoo Yokoyama
Various line fields naturally arise on surfaces in both physical and biological contexts, and generic singularities frequently appear in the form of 1-prong (thorn-like) and 3-pron…
Filtrations Indexed by Attracting Levels and their Applications
Yusuke Imoto, Tomoo Yokoyama
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data an…
Coarse chain recurrence, Morse graphs with finite errors, and persistence of circulations
Tomoo Yokoyama
This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical…
Topological flow data analysis for transient flow patterns: a graph-based approach
Takashi Sakajo, Takeshi Matsumoto, Shizuo Kaji +2
We introduce a method of time series analysis for two-dimensional transient flow patterns based on Topological Flow Data Analysis (TFDA), a new approach to topological data analysi…
Length averages for codimension one foliations
Masayuki Asaoka, Yushi Nakano, Paulo Varandas +1
In this paper we study geometrical and dynamical properties of codimension one foliations, by exploring a relation between length averages and ball averages of certain group action…
Relativistic helicity and link in Minkowski space-time
Z. Yoshida, Y. Kawazura, T. Yokoyama
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 convent…