Towards a global view of dynamical systems, for the C1-topology.

Christian Bonatti (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

This paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits Diff1(M) in disjoint C1-open regions whose union is C1-dense, and conjectures state that these open set, and their complement, are characterized by the presence of • either a robust local phenomenon • or a global structure forbiding this local phenomenon. Other conjectures states that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.

Mots clés: Diffeomorphisms; robust properties; hyperbolic structures

Domaines: Systèmes dynamiques [math.DS]

Christian Bonatti. Towards a global view of dynamical systems, for the C1-topology.. 2010. ⟨hal-00463421⟩