Simplicity of the group of compactly supported area preserving homeomorphisms of the open disc and fragmentation of symplectic diffeomorphisms

Frédéric Le Roux (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

In 1980, Albert Fathi asked whether the group of area-preserving homeomorphisms of the 2-disc that are the identity near the boundary is a simple group. In this paper, we show that the simplicity of this group is equivalent to the following fragmentation property in the group of compactly supported, area preserving diffeomorphisms of the plane: there exists a constant m such that every element supported on a disc D is the product of at most m elements supported on topological discs whose area are half the area of D.

Mots clés: symplectic diffeomorphisms; simple group; surface homeomorphism; hamiltonian dynamics; fragmentation; symplectic diffeomorphisms.

Domaines: Systèmes dynamiques [math.DS]; Géométrie symplectique [math.SG]

Frédéric Le Roux. Simplicity of the group of compactly supported area preserving homeomorphisms of the open disc and fragmentation of symplectic diffeomorphisms. 2009. ⟨hal-00353685⟩