Robust transitivity for endomorphisms admitting critical points

TL;DR

This paper investigates the conditions under which endomorphisms with critical points on the 2D torus are robustly transitive, providing examples and necessary conditions for such dynamical systems.

Contribution

It introduces new open examples of robustly transitive endomorphisms with persistent critical points and establishes necessary conditions for their robustness.

Findings

Existence of open sets of robustly transitive maps with critical points

Necessary conditions for robust transitivity in endomorphisms with critical points

Construction of examples in any isotopic class on the 2D torus

Abstract

We address the problem of giving necessary and sufficient conditions in order to have robustly transitive endomorphisms admitting persistent critical sets. We exhibit different type of open examples of robustly transitive maps in any isotopic class of endomorphisms acting on the two dimensional torus admitting persistent critical points. We also provide some necessary condition for robust transitivity in this setting.