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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2006

Perturbations of the derivative along periodic orbits

Résumé

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 C1-small perturbation along the orbit. As a consequence we show that the linear Poincaré flow of a C1-vector field admits a dominated splitting over any robustly transitive set.
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Dates et versions

hal-00387484 , version 1 (25-05-2009)

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  • HAL Id : hal-00387484 , version 1

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Christian Bonatti, Nicolas Gourmelon, Vivier Thérèse. Perturbations of the derivative along periodic orbits. Ergodic Theory and Dynamical Systems, 2006, 26 (5), pp.1307--1337. ⟨hal-00387484⟩
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