Reversibility and equivariance in center manifolds of nonautonomous dynamics

Pages: 677 - 699, Volume 18, Issue 4, August 2007

doi:10.3934/dcds.2007.18.677       Abstract        Full Text (285.2K)       Related Articles

Luís Barreira - Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (email)
Claudia Valls - Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (email)

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.

Keywords:  center manifolds, equivariance, nonuniform exponential trichotomies, reversibility.
Mathematics Subject Classification:  Primary: 34D09, 37D10, 37D25.

Received: June 2006;      Revised: January 2007;      Published: May 2007.