Tomoo Yokoyama - Generalizations of Morse Graph of Flows and Reeb Graph of Hamiltonian Flows

Explore a 28-minute lecture on generalizations of Morse graphs and Reeb graphs in dynamical systems. Delve into the connections between algebraic topology and flow analysis, covering topics such as reductions of dynamical systems, CW decompositions, and the detection of original flows from time-one maps. Learn about abstract weak orbits, Reeb graphs as abstract orbit spaces, and the relationship between Conley theory and Morse graphs. Gain insights into existing topological invariants of flows and fundamental notations used in the field. This talk, presented by Tomoo Yokoyama for the Applied Algebraic Topology Network, offers a comprehensive overview of advanced concepts in the study of flows and their topological representations.

Intro
Reductions of Reeb graphs to Barcodes
Reductions of dynamical systems to Morse graphs
Reductions of Morse flows to CW decompositions
Triviality of Morse graphs
Detection of original flows from the time one maps
Reeb graph for a function and the orbit space of it
Existing topological invariants of flows
Definitions recurrent point
Fundamental notations
Abstract weak orbit
Reeb graph as an abstract orbit space with binary relations
A generalization of a Morse graph and a Reeb graph
Conley theory and Morse graph