Partially hyperbolic surface endomorphisms

Abstract

We prove that a class of weakly partially hyperbolic endomorphisms on ${\mathbb{T}}^2$ are dynamically coherent and leaf conjugate to linear toral endomorphisms. Moreover, we give an example of a partially hyperbolic endomorphism on ${\mathbb{T}}^2$ which does not admit a centre foliation.

13 pages, 1 figure