Objectif This project is dedicated to the study of two distinct classes of dynamical systems which display a quasiperiodic component.The first class consists of quasiperiodic cocycles, and we will largely focus on connections with the spectral theory of quasiperiodic Schrodinger operators. Up to very recently, our understanding had been mostly restricted to situations where the potential would have some clear characteristics of large or small potentials. In particular, no genuinely global theory had been devised that could go so far as give insight on the phase-transition between large-like and small-like potentials. With the introduction by the PI of techniques to analyze the parameter dependence of one-frequency potentials which involve much less control of the dynamics of associated cocycles, and the discovery of new regularity features of this dependence, it is now possible to elaborate a precise conjectural global picture, whose proof is one of the major goals of the project.The second class consists of translation flows on higher genus surfaces. The Teichmuller flow acts as renormalization in this class, and its chaotic features have permitted a detailed description of the dynamics of typical translation flows. This project will concentrate on the the development of techniques suitable to the analysis of non-typical families of translation flows, which arise naturally in the context of certain applications, as for rational billiards. We aim to obtain results regarding the spectral gap for restrictions of the SL(2,R action, the existence of polynomial deviations outside exceptional cases, and the weak mixing property for certain billiards. Champ scientifique natural sciencesmathematicsapplied mathematicsdynamical systems Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Appel à propositions ERC-2010-StG_20091028 Voir d’autres projets de cet appel Régime de financement ERC-SG - ERC Starting Grant Institution d’accueil CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Contribution de l’UE € 1 020 840,00 Adresse RUE MICHEL ANGE 3 75794 Paris France Voir sur la carte Région Ile-de-France Ile-de-France Paris Type d’activité Research Organisations Contact administratif Julie Zittel (Ms.) Chercheur principal Artur Avila Cordeiro De Melo (Dr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS France Contribution de l’UE € 1 020 840,00 Adresse RUE MICHEL ANGE 3 75794 Paris Voir sur la carte Région Ile-de-France Ile-de-France Paris Type d’activité Research Organisations Contact administratif Julie Zittel (Ms.) Chercheur principal Artur Avila Cordeiro De Melo (Dr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée
