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Statistical stability for diffeomorphisms with dominated splitting

Published online by Cambridge University Press:  14 November 2006

CARLOS H. VÁSQUEZ
CARLOS H. VÁSQUEZ
Affiliation:
Universidad Católica del Norte, Departamento de Matemáticas, Casilla 1280, Antofagasta, Chile (e-mail: cavasquez@ucn.cl)
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Abstract

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Alves, Bonatti and Viana have recently shown that physical (or Sinai–Ruelle–Bowen) invariant measures exist for partially hyperbolic diffeomorphisms with mostly expanding center-unstable direction. In this paper we prove that such systems are statistically stable, that is, nearby diffeomorphisms have nearby physical measures.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 1 , February 2007 , pp. 253 - 283
Copyright
2006 Cambridge University Press