Noninvertible cocycles: Robustness of exponential dichotomies

Luis Barreira; Claudia Valls

doi:10.3934/dcds.2012.32.4111

Article Contents

2012, Volume 32, Issue 12: 4111-4131. Doi: 10.3934/dcds.2012.32.4111

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Noninvertible cocycles: Robustness of exponential dichotomies

Luis Barreira^1, and
Claudia Valls^2,

1.
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa
2.
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa

Received: May 31, 2010

Revised: April 30, 2012

Published: November 2012

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Abstract

For the dynamics defined by a sequence of bounded linear operators in a Banach space, we establish the robustness of the notion of exponential dichotomy. This means that an exponential dichotomy persists under sufficiently small linear perturbations. We consider the general cases of a nonuniform exponential dichotomy, which requires much less than a uniform exponential dichotomy, and of a noninvertible dynamics or, more precisely, of a dynamics that may not be invertible in the stable direction.

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Mathematics Subject Classification: Primary: 34D99, 37C75.

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