# American Institute of Mathematical Sciences

2007, 18(4): 677-699. doi: 10.3934/dcds.2007.18.677

## Reversibility and equivariance in center manifolds of nonautonomous dynamics

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

Received  June 2006 Revised  January 2007 Published  May 2007

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.
Citation: Luis Barreira, Claudia Valls. Reversibility and equivariance in center manifolds of nonautonomous dynamics. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 677-699. doi: 10.3934/dcds.2007.18.677
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