William Kalies, Florida Atlantic University

Abstract

Combinatorial representations of dynamical systems have been used to extract rigorous statements about global dynamics computationally. Recent results have addressed how robustly these representations may capture the underlying dynamical structure. Further development of these methods and algorithms relies on understanding the natural order structures in global dynamics related to attractors and Morse decompositions.

In this talk we present combinatorial order-theoretic models for global dynamics. We give computational examples that illustrate the theory for both maps and flows as well as applications to implicitly / imprecisely defined systems and systems measured from data. 

Video