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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the uniform hyperbolicity of some nonuniformly hyperbolic systems


Authors: José F. Alves, Vítor Araújo and Benoît Saussol
Journal: Proc. Amer. Math. Soc. 131 (2003), 1303-1309
MSC (2000): Primary 58F15, 58F99
Published electronically: November 20, 2002
MathSciNet review: 1948124
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Abstract: We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability (probability one with respect to every invariant probability measure) are necessarily uniformly expanding. We also present a version of this result for diffeomorphisms with nonuniformly hyperbolic sets.


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Additional Information

José F. Alves
Affiliation: Centro de Matemática da Universidade do Porto, 4169-007 Porto, Portugal
Email: jfalves@fc.up.pt

Vítor Araújo
Affiliation: Centro de Matemática da Universidade do Porto, 4169-007 Porto, Portugal
Email: vdaraujo@fc.up.pt

Benoît Saussol
Affiliation: LAMFA - Université de Picardie Jules Verne, 33 rue St Leu, 80039 Amiens, France
Email: benoit.saussol@u-picardie.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06857-0
PII: S 0002-9939(02)06857-0
Keywords: Nonuniformly expanding maps, uniformly expanding maps
Received by editor(s): November 21, 2001
Published electronically: November 20, 2002
Additional Notes: The authors were partially supported by PRODYN
Communicated by: Michael Handel
Article copyright: © Copyright 2002 American Mathematical Society