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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

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.

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

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