Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T01:11:11.941Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected])
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)