Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T15:05:25.373Z Has data issue: false hasContentIssue false
  • English
  • Français

Perturbations of the derivative along periodic orbits

Published online by Cambridge University Press:  11 September 2006

CHRISTIAN BONATTI ,
NIKOLAS GOURMELON  and
THÉRÈSE VIVIER
CHRISTIAN BONATTI
Affiliation:
IMB, UMR 5584 du CNRS, BP 47 870, 21078 Dijon Cedex, France (e-mail: [email protected], [email protected], [email protected])
NIKOLAS GOURMELON
Affiliation:
IMB, UMR 5584 du CNRS, BP 47 870, 21078 Dijon Cedex, France (e-mail: [email protected], [email protected], [email protected])
THÉRÈSE VIVIER
Affiliation:
IMB, UMR 5584 du CNRS, BP 47 870, 21078 Dijon Cedex, France (e-mail: [email protected], [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that a periodic orbit of large period of a diffeomorphism or flow either admits a dominated splitting of a prescribed strength or can be turned into a sink or a source by a $C^1$-small perturbation along the orbit. As a consequence we show that the linear Poincaré flow of a $C^1$-vector field admits a dominated splitting over any robustly transitive set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 5 , October 2006 , pp. 1307 - 1337
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.)