Transitive endomorphisms with critical points

TL;DR

This paper proves that certain non-wandering endomorphisms of the torus with generic critical points and no invariant directions are transitive, extending previous results by relaxing conditions on critical points and volume preservation.

Contribution

It introduces a broader class of toral endomorphisms for which transitivity is guaranteed, including those with critical points and without volume preservation.

Findings

Non-wandering endomorphisms with generic critical points are transitive.

The result generalizes previous work by Andersson.

The conditions on the linear part are relaxed to include non-invertible cases.

Abstract

We show that a non-wandering endomorphism of the torus with invertible linear part without invariant directions and for which the critical points are in some sense generic is transitive. This improves a result of Andersson by allowing critical points and improving the volume preserving assumption.