Reversibility and equivariance in center manifolds of nonautonomous dynamics

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 <em>nonuniformly partially hyperbolic dynamics</em>, corresponding to the existence of a nonuniform exponential trichotomy of the linear variational equation. We also consider the case of <em>nonautonomous dynamics</em>.