ﻻ يوجد ملخص باللغة العربية
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.
The two main results of this paper concern the regularity of the invariant foliation of a C0-integrable symplectic twist diffeomorphisms of the 2-dimensional annulus, namely that $bullet$ the generating function of such a foliation is C1 ; $bullet$ t
We generalize the hamiltonian topology on hamiltonian isotopies to an intrinsic symplectic topology on the space of symplectic isotopies. We use it to define the group $SSympeo(M,omega)$ of strong symplectic homeomorphisms, which generalizes the grou
We provide a new geometric proof of Reimanns theorem characterizing quasiconformal mappings as the ones preserving functions of bounded mean oscillation. While our proof is new already in the Euclidean spaces, it is applicable in Heisenberg groups as
We study an equation lying `mid-way between the periodic Hunter-Saxton and Camassa-Holm equations, and which describes evolution of rotators in liquid crystals with external magnetic field and self-interaction. We prove that it is an Euler equation o
A group $G$ is said to be periodic if for any $gin G$ there exists a positive integer $n$ with $g^n=id$. We prove that a finitely generated periodic group of homeomorphisms on the 2-torus that preserves a measure $mu$ is finite. Moreover if the group