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Existence of SRB-measures for some topologically hyperbolic diffeomorphisms

Published online by Cambridge University Press:  09 August 2004

RENAUD LEPLAIDEUR
RENAUD LEPLAIDEUR
Affiliation:
Laboratoire de Mathématiques, Université de Bretagne Occidentale, 6 rue Victor Le Gorgeu, BP 809, F-29285 Brest Cedex, France (e-mail: [email protected])
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Abstract

A diffeomorphism f of a compact manifold M is called almost Axiom-A if it is hyperbolic in a neighborhood of some compact f-invariant set $\Omega$, 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 and such that for every point in this set the stable and unstable leaves are ‘long enough’, then f admits either a probability Sinai–Ruelle–Bowen (SRB)-measure or a $\sigma$-finite SRB-measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 4 , August 2004 , pp. 1199 - 1225
Copyright
2004 Cambridge University Press

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