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NONUNIFORM EXPONENTIAL BEHAVIOUR AND TOPOLOGICAL EQUIVALENCE

Published online by Cambridge University Press:  21 July 2015

LUIS BARREIRA
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal e-mail: [email protected]
LIVIU HORIA POPESCU
Affiliation:
Department of Mathematics and Informatics, Oradea University, Str. Universitatii Nr.1, 410087 Oradea, Romania e-mail: [email protected]
CLAUDIA VALLS
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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