Topological and smooth classification of Anosov maps on torus

2022/12/22 by Gu, Ruihao, Shi, Yi
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.11457

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.

Related

• Geometric growth for Anosov maps on the 3 torus
• Regularity of Non-stationary Stable Foliations of Toral Anosov Maps
• Rigidity for Some Cases of Anosov Endomorphisms of Torus
• Smooth rigidity for 3-dimensional dissipative Anosov flows
• Smooth rigidity for very non-algebraic Anosov diffeomorphisms of codimension one