Lyapunov functions and expansive diffeomorphisms on 3D-manifolds

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Abstract

Let M be a three-dimensional compact connected oriented manifold and f : M \rightarrow M an expansive diffeomorphism. We prove that non-wandering points have local stable or unstable sets locally separating M. This property allows us to prove that if \Omega(f)=M then f is conjugate to a linear Anosov diffeomorphism and M=T^3, the three-dimensional torus.

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