Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T04:42:26.322Z Has data issue: false hasContentIssue false
  • English
  • Français

Center manifolds for non-uniformly partially hyperbolic trajectories

Published online by Cambridge University Press:  14 November 2006

LUIS BARREIRA  and
CLAUDIA VALLS
LUIS BARREIRA
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (e-mail: [email protected], [email protected])
CLAUDIA VALLS
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (e-mail: [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We establish the existence of center manifolds for a class of non-uniformly partially hyperbolic trajectories of non-autonomous ordinary differential equations $v'=A(t)v+f(t,v)$ on Banach spaces. In particular, we allow the stable and unstable components of $v'=A(t)v$ to exhibit non-uniform contraction and expansion along the trajectory. We also allow the center component to exhibit non-uniform behavior. To the best of our knowledge, we establish the first center manifold theorem in the non-uniform setting.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 6 , December 2006 , pp. 1707 - 1732
Copyright
2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)