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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Robust ergodic properties in partially hyperbolic dynamics


Author: Martin Andersson
Journal: Trans. Amer. Math. Soc. 362 (2010), 1831-1867
MSC (2000): Primary 37D25, 37D30, 37C40
Published electronically: November 18, 2009
MathSciNet review: 2574879
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Abstract: We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti and Viana (2000) about existence and finitude of physical measures is extended to the case of local diffeomorphisms. Moreover, we prove that such systems constitute a $ C^2$-open set in which statistical stability is a dense property. In contrast, all mostly contracting systems are shown to be stable under small random perturbations.


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Additional Information

Martin Andersson
Affiliation: Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brasil
Address at time of publication: Departamento de Matemática Aplicada, Universidade Federal Fluminense, Rua Mário Santos Braga, s/n, Campus do Valonguinho, 24020-140, Centro Niterói - RJ Brazil
Email: martin@mat.uff.br

DOI: http://dx.doi.org/10.1090/S0002-9947-09-05027-2
PII: S 0002-9947(09)05027-2
Keywords: Physical measures, statistical stability, stochastic stability
Received by editor(s): August 20, 2007
Published electronically: November 18, 2009
Additional Notes: This work was supported by CNPq (Brazil)
Article copyright: © Copyright 2009 by the author