8 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…
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…
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…
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 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…
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…