Analytic invariant manifolds for sequences of diffeomorphisms |
| |
Authors: | Luis Barreira Claudia Valls |
| |
Institution: | Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal |
| |
Abstract: | We obtain real analytic invariant manifolds for trajectories of maps assuming only the existence of a nonuniform exponential behavior. We also consider the more general case of sequences of maps, which corresponds to a nonautonomous dynamics with discrete time. We emphasize that the maps that we consider are defined in a real Euclidean space, and thus, one is not able to obtain the invariant manifolds from a corresponding procedure to that in the nonuniform hyperbolicity theory in the context of holomorphic dynamics. We establish the existence both of stable (and unstable) manifolds and of center manifolds. As a byproduct of our approach we obtain an exponential control not only for the trajectories on the invariant manifolds, but also for all their derivatives. |
| |
Keywords: | 37D10 37D25 |
本文献已被 ScienceDirect 等数据库收录! |
|