Wrapped Floer homology and hyperbolic sets

TL;DR

This paper explores the relationship between wrapped Floer homology barcodes and topological entropy, establishing a lower bound for barcode entropy in the presence of hyperbolic sets for Reeb flows.

Contribution

It introduces a new lower bound for wrapped Floer homology barcode entropy based on topological entropy within hyperbolic sets for Reeb flows.

Findings

Wrapped Floer homology barcode entropy is bounded below by topological entropy.

The study links Floer homology invariants with dynamical complexity measures.

Provides new insights into the interplay between symplectic topology and dynamical systems.

Abstract

In this paper, we continue the quest to understand the interplay between wrapped Floer homology barcode and topological entropy. Wrapped Floer homology barcode entropy is defined as the exponential growth, with respect to the left endpoints, of the number of not-too-short bars in its barcode. We prove that, in the presence of a topologically transitive, locally maximal hyperbolic set for the Reeb flow on the boundary of a Liouville domain, the barcode entropy is bounded from below by the topological entropy restricted to the hyperbolic set.