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Groupes de Schottky et comptage

Jean-François Quint (2005)

Annales de l’institut Fourier

Soient X un espace symétrique de type non compact et Γ un groupe discret d’isométries de X du type de Schottky. Dans cet article, nous donnons des équivalents des fonctions orbitales de comptage pour l’action de Γ sur X .

Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function

Yoshifumi Matsuda (2009)

Annales de l’institut Fourier

We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the C 1 -topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic subgroup of finite index or a nonabelian free subgroup.

Growth conditions for the stability of a class of time-varying perturbed singular systems

Faten Ezzine, Mohamed Ali Hammami (2022)

Kybernetika

In this paper, we investigate the problem of stability of linear time-varying singular systems, which are transferable into a standard canonical form. Sufficient conditions on exponential stability and practical exponential stability of solutions of linear perturbed singular systems are obtained based on generalized Gronwall inequalities and Lyapunov techniques. Moreover, we study the problem of stability and stabilization for some classes of singular systems. Finally, we present a numerical example...

Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation

Marcel Guardia, Vadim Kaloshin (2015)

Journal of the European Mathematical Society

We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix s > 1 . Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence of solutions with s -Sobolev norm growing in time. We establish the existence of solutions with polynomial time estimates. More exactly, there is c > 0 such that for any 𝒦 1 we find a solution u and a time T such that u ( T ) H s 𝒦 u ( 0 ) H s . Moreover, the time T satisfies the polynomial bound 0 < T < 𝒦 C .

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