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SRB measures for almost Axiom A diffeomorphisms

Published online by Cambridge University Press:  19 March 2015

JOSÉ F. ALVES  and
RENAUD LEPLAIDEUR
JOSÉ F. ALVES
Affiliation:
Departamento de Matemática, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal email [email protected]
RENAUD LEPLAIDEUR
Affiliation:
LMBA UMR 6205, Université de Brest, 6 Av. Victor Le Gorgeu, C.S. 93837, 29238 Brest cedex 3, France email [email protected]
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Abstract

We consider a diffeomorphism $f$ of a compact manifold $M$ which is almost Axiom A, i.e. $f$ is hyperbolic in a neighborhood of some compact $f$-invariant set, except in some singular set of neutral points. We prove that if there exists some $f$-invariant set of hyperbolic points with positive unstable Lebesgue measure such that for every point in this set the stable and unstable leaves are ‘long enough’, then $f$ admits an SRB (probability) measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 7 , October 2016 , pp. 2015 - 2043
Copyright
© Cambridge University Press, 2015 

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