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

Andrey Gogolev; Misha Guysinsky

doi:10.3934/dcds.2008.22.183

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2008, Volume 22, Issue 1&2: 183-200. Doi: 10.3934/dcds.2008.22.183

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

Andrey Gogolev^1, and
Misha Guysinsky^1,

1.
109 McAllister Bldg., University Park, PA 16802

Received: July 31, 2007

Revised: September 30, 2007

Published: February 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 37C15, 37D20; Secondary: 34D10.

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