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Conjugacies for impulsive equations

Part of: Smooth dynamical systems: general theory Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  01 November 2011

Luis Barreira  and
Claudia Valls
Luis Barreira
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049001 Lisboa, Portugal (barreira@math.ist.utl.pt; cvalls@math.ist.utl.pt)
Claudia Valls
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049001 Lisboa, Portugal (barreira@math.ist.utl.pt; cvalls@math.ist.utl.pt)
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Abstract

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For impulsive differential equations, we construct topological conjugacies between linear and nonlinear perturbations of non-uniform exponential dichotomies. In the case of linear perturbations, the topological conjugacies are constructed in a more or less explicit manner. In the nonlinear case, we obtain an appropriate version of the Grobman–Hartman Theorem for impulsive equations, with a simple and direct proof that involves no discretization of the dynamics.

Keywords

Grobman–Hartman Theoremtopological conjugaciesimpulsive equations

MSC classification

Secondary: 37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 65 - 78
Copyright
Copyright © Edinburgh Mathematical Society 2011

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