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NONUNIFORM EXPONENTIAL BEHAVIOUR AND TOPOLOGICAL EQUIVALENCE

Part of: Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  21 July 2015

LUIS BARREIRA ,
LIVIU HORIA POPESCU  and
CLAUDIA VALLS
LUIS BARREIRA
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal e-mail: barreira@math.ist.utl.pt
LIVIU HORIA POPESCU
Affiliation:
Department of Mathematics and Informatics, Oradea University, Str. Universitatii Nr.1, 410087 Oradea, Romania e-mail: lpopescu2002@yahoo.com
CLAUDIA VALLS
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal e-mail: cvalls@math.ist.utl.pt
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Abstract

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We show that any evolution family with a strong nonuniform exponential dichotomy can always be transformed by a topological equivalence to a canonical form that contracts and/or expands the same in all directions. We emphasize that strong nonuniform exponential dichotomies are ubiquitous in the context of ergodic theory. The main novelty of our work is that we are able to control the asymptotic behaviour of the topological conjugacies at the origin and at infinity.

MSC classification

Primary: 37D10: Invariant manifold theory
Secondary: 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 2 , May 2016 , pp. 279 - 291
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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