Uniform hyperbolic approximations of measures with non-zero Lyapunov exponents

Authors:
Stefano Luzzatto and Fernando J. Sánchez-Salas

Journal:
Proc. Amer. Math. Soc. **141** (2013), 3157-3169

MSC (2010):
Primary 37D25

Published electronically:
May 24, 2013

MathSciNet review:
3068969

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Abstract: We show that for any diffeomorphism of a compact Riemannian manifold, every non-atomic, ergodic, invariant probability measure with non-zero Lyapunov exponents is approximated by uniformly hyperbolic sets in the sense that there exists a sequence of compact, topologically transitive, locally maximal, uniformly hyperbolic sets such that for any sequence of -invariant ergodic probability measures with we have in the weak- topology.

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Additional Information

**Stefano Luzzatto**

Affiliation:
Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy

Email:
luzzatto@ictp.it

**Fernando J. Sánchez-Salas**

Affiliation:
Departamento de Matemáticas, Facultad Experimental de Ciencias, Universidad del Zulia, Avenida Universidad, Edificio Grano de Oro, Maracaibo, Venezuela

Email:
fjss@fec.luz.edu.ve

DOI:
http://dx.doi.org/10.1090/S0002-9939-2013-11565-0

Keywords:
Non-uniformly hyperbolic systems,
uniformly hyperbolic systems,
approximation of hyperbolic measures

Received by editor(s):
June 7, 2011

Received by editor(s) in revised form:
July 14, 2011, and November 25, 2011

Published electronically:
May 24, 2013

Additional Notes:
Most of this work was carried out at the Abdus Salam International Centre for Theoretical Physics (ICTP). The second author was partially supported by the Associateship Programme of ICTP

Communicated by:
Bryna Kra

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.