Topological Entropy of Hamiltonian Systems and Persistence Modules

by Prof. Basak Gürel (University of Central Florida)

Tuesday 28 May 2024, 17:00 → 19:00 Europe/Berlin

Topological entropy is a fundamental invariant of a dynamical system, measuring its complexity. In this talk, we discuss connections between the topological entropy of a Hamiltonian system, e.g., a geodesic flow, and the underlying filtered Morse or Floer homology viewed as a persistence module in the spirit of Topological Data Analysis. We introduce barcode entropy — a Morse/Floer theoretic counterpart of topological entropy — and show that barcode entropy is closely related to topological entropy and that, in low dimensions, these invariants agree. For instance, for a geodesic flow on any closed surface, the barcode entropy is equal to the topological entropy. The talk is based on joint work with Erman Cineli, Viktor Ginzburg, and Marco Mazzucchelli.