Transitivity of codimension one non-invertible conservative skew-products

TL;DR

This paper investigates the conditions under which volume-preserving skew-products on the n-torus are transitive, linking this property to their induced action on the fundamental group.

Contribution

It establishes a relationship between transitivity of volume-preserving skew-products and their induced action on the fundamental group.

Findings

Transitivity is characterized by the induced action on the fundamental group.

Conditions for transitivity depend on the properties of the skew-product's action.

The work extends understanding of dynamical behavior in non-invertible conservative systems.

Abstract

In this work we explore the problem of transitivity of volume-preserving skew-products endomorphisms of the n-torus. More specifically, we establish relationships between transitivity and the action induced by the skew-product in the fundamental group.