Dynamically Incoherent Surface Endomorphisms

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