Transitivity of conservative toral endomorphisms

Abstract

It is shown that if a non-invertible area preserving local homeomorphism on ${\mathbb{T}}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in any smoothness category, of those homotopy classes of conservative endomorphisms that consist entirely of transitive maps.

11 pages

Cited by in corpus (5)

• Transitivity of codimension one non-invertible conservative skew-products
• Non-uniformly hyperbolic endomorphisms
• High dimensional robustly singular maps that are $C^1$ robustly transitive
• Topology of pre-images under Anosov endomorphisms
• Transitivity of conservative diffeomorphisms isotopic to Anosov on ${\mathbb{T}}^3$