Robustly N-expansive surface diffeomorphisms

TL;DR

This paper establishes conditions under which surface diffeomorphisms are robustly N-expansive and cw-expansive, providing examples that are not Anosov but still exhibit these properties, expanding understanding of surface dynamics.

Contribution

It introduces new sufficient conditions for robust N-expansiveness and cw-expansiveness on compact surfaces, with explicit examples beyond Anosov systems.

Findings

Identifies conditions for robust N-expansiveness and cw-expansiveness.

Provides examples on genus two surfaces with non-Anosov diffeomorphisms.

Shows these systems can have tangencies at wandering points.

Abstract

We give sufficient conditions for a diffeomorphism of a compact surface to be robustly $N$-expansive and cw-expansive in the $C^r$-topology. We give examples on the genus two surface showing that they need not to be Anosov diffeomorphisms. The examples are axiom A diffeomorphisms with tangencies at wandering points.