%0 Journal Article
%T On the Unstable Directions and Lyapunov Exponents of Anosov Endomorphisms
%A F. Micena
%A A. Tahzibi
%J Mathematics
%D 2014
%I arXiv
%X Despite the invertible setting, Anosov endomorphisms may have infinitely many unstable directions. Here we prove, under transitivity assumption, that an Anosov endomorphism on a closed manifold $M,$ is either special (that is, every $x \in M$ has only one unstable direction) or for a typical point in $M$ there are infinitely many unstable directions. Other result of this work is the semi rigidity of the unstable Lyapunov exponent of a $C^{1+\alpha}$ codimension one Anosov endomorphism and $C^1$ close to a linear endomorphism of $\mathbb{T}^n$ for $(n \geq 2).$ In the appendix we give a proof for ergodicity of $C^{1+\alpha}, \alpha > 0,$ conservative Anosov endomorphism.
%U http://arxiv.org/abs/1412.0629v1