Dynamically incoherent surface endomorphisms

Abstract

We explicitly construct a dynamically incoherent partially hyperbolic endomorphisms of ${\mathbb{T}}^2$ in the homotopy class of any linear expanding map with integer eigenvalues. These examples exhibit branching of centre curves along countably many circles, and thus exhibit a form of coherence that has not been observed for invertible systems.

arXiv comment18 pages, 6 figures