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On the uniform hyperbolicity of some nonuniformly hyperbolic systems
Author(s):
José
F.
Alves;
Vítor
Araújo;
Benoît
Saussol
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1303-1309.
MSC (2000):
Primary 58F15, 58F99
Posted:
November 20, 2002
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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:
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
Posted:
November 20, 2002
Additional Notes:
The authors were partially supported by PRODYN
Communicated by:
Michael Handel
Copyright of article:
Copyright
2002,
American Mathematical Society
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