Soient $X$ un espace symétrique de type non compact et $\Gamma$ 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 $\Gamma$ sur $X$.

The purpose of this paper is to prove the existence of a symplectic realization for a large class of regular Poisson manifolds with Riemannian two dimensional characteristic foliation. To do so, we will show that the homotopy groupoid of a Riemannian foliation is locally trivial.

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.

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...

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 $𝒦\gg 1$ we find a solution $u$ and a time $T$ such that ${\parallel u\left(T\right)\parallel }_{H^s}\ge 𝒦{\parallel u\left(0\right)\parallel }_{H^s}$. Moreover, the time $T$ satisfies the polynomial bound $0<T<{𝒦}^C$.