Statistical stability for diffeomorphisms with dominated splitting

Carlos H. Vásquez

doi:10.1017/S0143385706000721

Statistical stability for diffeomorphisms with dominated splitting

Carlos H. Vásquez

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

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.

Original language	English
Pages (from-to)	253-283
Number of pages	31
Journal	Ergodic Theory and Dynamical Systems
Volume	27
Issue number	1
DOIs	https://doi.org/10.1017/S0143385706000721
State	Published - Feb 2007
Externally published	Yes

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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.",

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AB - 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.

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Statistical stability for diffeomorphisms with dominated splitting

Abstract

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