6533b858fe1ef96bd12b59ce

RESEARCH PRODUCT

Perturbations of the derivative along periodic orbits

Christian BonattiNikolas GourmelonThérèse Vivier

subject

Applied MathematicsGeneral Mathematics[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]010102 general mathematicsMathematical analysis[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Transitive set16. Peace & justice01 natural sciences37D30 (34C25 34D10 37C05 37C10 37C27)010101 applied mathematicsPeriodic orbitsVector fieldDiffeomorphism0101 mathematicsMathematics

description

International audience; 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.

yearjournalcountryeditionlanguage
2006-09-11
https://hal.archives-ouvertes.fr/hal-00387484