Topological and smooth classification of Anosov maps on torus

In this talk, we give a complete topological classification of non-invertible Anosov maps on torus. We show that two non-invertible Anosov maps on torus are topologically conjugate if and only if their corresponding periodic points have the same Lyapunov exponents on the stable bundles. As a corollary, if two non-invertible Anosov maps on torus are topologically conjugate, then the conjugacy is smooth along the stable foliation. We also give a smooth classification via Jacobian on corresponding periodic points.
This is a joint work with Ruihao Gu.