Invariant manifolds of partially normally hyperbolic invariant manifolds in Banach spaces

arXiv1905.09764MaRDI QIDQ6319256

Publication date: 23 May 2019

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.

Mathematics Subject Classification ID

Infinite-dimensional manifolds (58B99) Invariant manifold theory for dynamical systems (37D10) Partially hyperbolic systems and dominated splittings (37D30) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

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