Reversibility and equivariance in center manifolds of nonautonomous dynamics
Luís Barreira - 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
Received: June 2006; Revised: January 2007; Published: May 2007.
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