Topological and smooth classification of Anosov maps on torus

Abstract

In this paper, we give a complete topological and smooth 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 $C^r$ non-invertible Anosov maps on torus are topologically conjugate, then the conjugacy is $C^r$-smooth along the stable foliation. Moreover, we show that the smooth conjugacy class of a non-invertible Anosov map on torus is completely determined by the Jacobians of return maps at periodic points.

46 pages, 4 figures

References in corpus (1)

• Rigidity of stable Lyapunov exponents and integrability for Anosov maps

Cited by in corpus (1)

• Anosov Endomorphisms on the 2-torus: Regularity of foliations and rigidity