A generalized pseudo-rotation with positive topological entropy

TL;DR

This paper constructs Hamiltonian diffeomorphisms that are dynamically complex with positive topological entropy but exhibit minimal Floer-theoretic complexity, having only infinite bars in their Floer barcode.

Contribution

It introduces examples of Hamiltonian diffeomorphisms with positive topological entropy that are minimal from a Floer-theoretic perspective, showing a novel coexistence of complexity and minimality.

Findings

Existence of Hamiltonian diffeomorphisms with positive topological entropy

Floer barcode of all iterates contains only infinite bars

Maps have zero barcode entropy

Abstract

In this note we give examples of Hamiltonian diffeomorphisms which are on one hand dynamically complicated, for instance with positive topological entropy, and on the other hand minimal from the perspective of Floer theory. The minimality is in the sense that the barcode of the Floer complex of all iterates of these maps consists of only infinite bars. In particular, the maps have zero barcode entropy.