Ergodic Theory and Dynamical Systems

Perturbations of the derivative along periodic orbits

a1 IMB, UMR 5584 du CNRS, BP 47 870, 21078 Dijon Cedex, France (e-mail:,,

Article author query
bonatti c   [Google Scholar] 
gourmelon n   [Google Scholar] 
vivier t   [Google Scholar] 


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.

(Published Online September 11 2006)
(Received October 1 2004)
(Revised January 8 2006)