Quasi-periodic solutions of Hamiltonian PDEs
We overview recent existence results and techniques about KAM theory for PDEs.
Quasi-periodic solutions with Sobolev regularity of NLS on with a multiplicative potential
We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on , finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are then the solutions are . The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators...
Quasistable gradient and Hamiltonian systems with a pairwise interaction randomly perturbed by Wiener processes.
Quelques Commentaires Sur Le Plongement Des Difféomorphismes Locaux Du Plan.
Quelques invariants topologiques en géométrie symplectique
Quelques nouveaux invariants des difféomorphismes Morse--Smale d'une surface
Soit un difféomorphisme Morse-Smale d’une surface fermée. À une courbe instable de comportement 1 par rapport à un attracteur de correspond une courbe fermée sur un des tores (Bassin. Cette remarque nous permettra de définir de nouveaux invariants de conjugaison de . Nous en déduisons aussi un moyen d’écrire explicitement une puissance de comme le produit du temps 1 d’un champ de vecteurs Morse-Smale topologique par des isotopies à support des disques et des twists de Dehn de supports...
Quelques propriétés des lignes critiques d'une récurrence du second ordre à inverse non unique. Détermination d'une zone absorbante
Quelques résultats sur la dimension de Hausdorff des ensembles de Julia des polynômes quadratiques
This paper deals with the Hausdorff dimension of the Julia set of quadratic polynomials. It is divided in two parts. The first aims to compute good numerical approximations of the dimension for hyperbolic points. For such points, Ruelle’s thermodynamical formalism applies, hence computing the dimension amounts to computing the zero point of a pressure function. It is this pressure function that we approximate by a Monte-Carlo process combined with a shift method that considerably decreases the computational...
Questions about Polynomial Matings
We survey known results about polynomial mating, and pose some open problems.
Random data Cauchy problem for supercritical Schrödinger equations
Random dynamics and its applications.
Random entropy and recurrence.
Random mappings with a single absorbing center and combinatorics of discretizations of the logistic mapping.
Random matrices and permutations, matrix integrals and integrable systems
Random orderings and unique ergodicity of automorphism groups
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations...
Random permutations and unique fully supported ergodicity for the Euler adic transformation
There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations.
Random perturbations and statistical properties of Hénon-like maps
Randomly connected dynamical systems - asymptotic stability
We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.
Rank gradient, cost of groups and the rank versus Heegaard genus problem
We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the ‘rank vs. Heegaard genus’ conjecture on hyperbolic 3-manifolds is incompatible with the ‘fixed price problem’ in topological dynamics.
Rank-one group actions with simple mixing -subactions.