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February  2008, 22(1&2): 183-200. doi: 10.3934/dcds.2008.22.183

$C^1$-differentiable conjugacy of Anosov diffeomorphisms on three dimensional torus

Andrey Gogolev 1, and  Misha Guysinsky 1,

1. 

109 McAllister Bldg., University Park, PA 16802, United States, United States

Received  August 2007 Revised  October 2007 Published  June 2008

We consider two $C^2$ Anosov diffeomorphisms in a $C^1$ neighborhood of a linear hyperbolic automorphism of three dimensional torus with real spectrum. We prove that they are $C^{1+\nu}$ conjugate if and only if the differentials of the return maps at corresponding periodic points have the same eigenvalues.
Keywords: Anosov diffeomorphism, smooth conjugacy, periodic data..
Mathematics Subject Classification: Primary: 37C15, 37D20; Secondary: 34D1.
Citation: Andrey Gogolev, Misha Guysinsky. $C^1$-differentiable conjugacy of Anosov diffeomorphisms on three dimensional torus. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 183-200. doi: 10.3934/dcds.2008.22.183
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