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Start Over Author "Roux, Frédéric Le" Topic [math.math-sg]mathematics [math]/symplectic geometry [math.sg]
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1. Simplicity of the group of compactly supported area preserving homeomorphisms of the open disc and fragmentation of symplectic diffeomorphisms

Author

Roux, Frédéric Le, Laboratoire de Mathématiques d'Orsay (LM-Orsay), and Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematics - Symplectic Geometry, fragmentation, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], symplectic diffeomorphisms, 37E30, 57S99, 28D15, simple group, Mathematics - Dynamical Systems, hamiltonian dynamics, surface homeomorphism, [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG]
Abstract

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.

Published
2009

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