Topological Entropy of Reeb Flows, Barcodes and Floer Theory

Abstract: Topological entropy is one of the fundamental invariants of a dynamical system, measuring its complexity. In this talk, we focus on connections between the topological entropy of a Hamiltonian dynamical system, e.g., a Hamiltonian diffeomorphism or a Reeb or geodesic flow, and its Symplectic/Floer homology. We recall the definition of barcode entropy — a Floer theoretic counterpart of topological entropy — and discuss possible ways to extend it to Reeb flows. The talk is based on joint work with Erman Cineli, Basak Gurel and Marco Mazzucchelli.

differential geometrydynamical systemsgeometric topologysymplectic geometryspectral theory

Audience: researchers in the topic

Geometry and Dynamics seminar

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