Topological and smooth classification of Anosov maps on torus
| Autor: | Gu, Ruihao, Shi, Yi |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 46 pages, 4 figures |
| Databáze: | arXiv |
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