Reversibility and equivariance in center manifolds of nonautonomous dynamics

Luis Barreira; Claudia Valls

doi:10.3934/dcds.2007.18.677

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2007, Volume 18, Issue 4: 677-699. Doi: 10.3934/dcds.2007.18.677

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Reversibility and equivariance in center manifolds of nonautonomous dynamics

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, 2006

Revised: December 31, 2006

Published: September 2007

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Abstract

We consider reversible and equivariant dynamical systems in Banach spaces, either defined by maps or flows. We show that for a reversible (respectively, equivariant) system, the dynamics on any center manifold in a certain class of graphs (namely $C^1$ graphs with Lipschitz first derivative) is also reversible (respectively, equivariant). We consider the general case of center manifolds for a nonuniformly partially hyperbolic dynamics, corresponding to the existence of a nonuniform exponential trichotomy of the linear variational equation. We also consider the case of nonautonomous dynamics.

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Mathematics Subject Classification: Primary: 34D09, 37D10, 37D25.

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