Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group.
Groupes de Schottky et comptage
Soient un espace symétrique de type non compact et un groupe discret d’isométries de du type de Schottky. Dans cet article, nous donnons des équivalents des fonctions orbitales de comptage pour l’action de sur .
Groupoïde d'homotopie d'un feuilletage Riemannien et réalisation symplectique de certaines variétés de Poisson.
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.
Groupoïdes symplectiques
Groups acting on products of trees, tiling systems and analytic -theory.
Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function
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 -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
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
We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix . Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence of solutions with -Sobolev norm growing in time. We establish the existence of solutions with polynomial time estimates. More exactly, there is such that for any we find a solution and a time such that . Moreover, the time satisfies the polynomial bound .
Gyration numbers for involutions of subshifts of finite type II.
Gyration numbers for involutions of subshifts of finite type I.
Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold
We study the high-energy eigenfunctions of the Laplacian on a compact Riemannian manifold with Anosov geodesic flow. The localization of a semiclassical measure associated with a sequence of eigenfunctions is characterized by the Kolmogorov-Sinai entropy of this measure. We show that this entropy is necessarily bounded from below by a constant which, in the case of constant negative curvature, equals half the maximal entropy. In this sense, high-energy eigenfunctions are at least half-delocalized....
Hamiltonian Diffeomorphisms and Lagrangian Distributions.
Hamiltonian flows of curves in and vector soliton equations of mKdV and sine-Gordon type.
Hamiltonian loops from the ergodic point of view
Let be the group of Hamiltonian diffeomorphisms of a closed symplectic manifold . A loop is called strictly ergodic if for some irrational number the associated skew product map defined by is strictly ergodic. In the present paper we address the following question. Which elements of the fundamental group of can be represented by strictly ergodic loops? We prove existence of contractible strictly ergodic loops for a wide class of symplectic manifolds (for instance for simply connected...
Hamiltonian stability and subanalytic geometry
In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Using theorems of real subanalytic geometry, we derive a geometric criterion for steepness: a numerical function which is real analytic around a...
Hamiltonian structure and new exact soliton solutions of some Korteweg--de Vries equations.
Hamiltonian structure of pi hierarchy.
Hamiltonian Systems: Generic Properties of Closed Orbits and Local Perturbations.
Hamiltonian systems, Lagrangian tori and Birkhoffs's theorem.
Hamiltonian systems with linear potential and elastic constraints
We consider a class of Hamiltonian systems with linear potential, elastic constraints and arbitrary number of degrees of freedom. We establish sufficient conditions for complete hyperbolicity of the system.