Invariant manifolds of partially normally hyperbolic invariant manifolds in Banach spaces

2019/05/23 by Chen, Deliang
#37C05 #37D10 #37D30 #37L10 #58B99 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.09764

Abstract

We investigate the existence and regularity of (locally) invariant manifolds nearby an approximately invariant set satisfying certain (geometric) hyperbolicity with respect to an abstract `generalized' dynamical system in a Banach space; such hyperbolicity is between normal hyperbolicity and partial hyperbolicity which has being studied in the finite-dimension and in some concrete PDEs. The `generalized' dynamical system is allowed to be non-smooth, non-Lipschitz, or even `non-mapping', making it applicable to both well-posed and ill-posed differential equations. As an illustration, we apply our results to study the dynamics of the whiskered tori.

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