Differentiable Conjugacy of Anosov Diffeomorphisms on Three Dimensional Torus

Andrey Gogolev, Misha Guysinsky

Published 2008-02-12, updated 2008-09-02Version 2

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+ conjugate if and only if the differentials of the return maps at corresponding periodic points have the same eigenvalues.