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Lyapunov functions and expansive diffeomorphisms on 3D-manifolds

Published online by Cambridge University Press:  07 May 2002

JOSÉ L. VIEITEZ
JOSÉ L. VIEITEZ
Affiliation:
Facultad de Ingeniería, IMERL, Montevideo, Uruguay (e-mail: jlvb@fing.edu.uy)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 2 , April 2002, pp. 601 - 632
Copyright
2002 Cambridge University Press