Ensembles invariants non enlac�s des diff�omorphismes du tore et de l?anneau

Abstract

We introduce the notion of unlinked invariant set for a diffeomorphism of the 2-torus or the closed annulus and we look at the properties of these sets which generalize the Aubry-Mather sets. We prove that for any irrational number ρ in the rotation set of an area-preserving diffeomorphism of the annulus, there exists an unliked invariant set whose rotation set is reduced to ρ. In the same way we prove that any minimal diffeomorphism of the 2-torus homotopic to the identity may be approximated in the C0-topology by a periodic diffeomorphism.