Transitivity and topological mixing for C1 diffeomorphisms

Flavio Abdenur (1) , Sylvain Crovisier (2)

1 Departamento de Matematica
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We prove that, on connected compact manifolds, both C1-generic conservative diffeomorphisms and C1-generic transitive diffeomorphisms are topologically mixing. This is obtained through a description of the periods of a homoclinic class and by a control of the period of the periodic points given by the closing lemma.

Domaines: Systèmes dynamiques [math.DS]

Flavio Abdenur, Sylvain Crovisier. Transitivity and topological mixing for C1 diffeomorphisms. 2011. ⟨hal-00728289⟩