6533b831fe1ef96bd12999ab

RESEARCH PRODUCT

Recurrence and genericity

Sylvain CrovisierChristian Bonatti

subject

Pure mathematicsMathematics::Dynamical SystemsRiemann manifold[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)01 natural sciences37C05 37C20FOS: Mathematics0101 mathematicsMathematics - Dynamical SystemsDynamical system (definition)Mathematics::Symplectic GeometryMathematicsLemma (mathematics)Transitive relationRecurrence relationgeneric properties010102 general mathematicsMathematical analysissmooth dynamical systemsGeneral Medicine16. Peace & justicechain recurrence010101 applied mathematicsconnecting lemmaDiffeomorphism

description

We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative diffeomorphisms are transitive. Nous montrons un lemme de connexion C^1 pour les pseudo-orbites des diffeomorphismes des varietes compactes. Nous explorons alors les consequences pour les diffeomorphismes C^1-generiques. Par exemple, les diffeomorphismes conservatifs C^1-generiques sont transitifs.

yearjournalcountryeditionlanguage
2003-06-26
https://hal.archives-ouvertes.fr/hal-00000449