Obiettivo 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. Campo scientifico natural sciencesmathematicsapplied mathematicsdynamical systems Programma(i) 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) Argomento(i) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Invito a presentare proposte ERC-2010-StG_20091028 Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-SG - ERC Starting Grant Istituzione ospitante CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Contributo UE € 1 020 840,00 Indirizzo RUE MICHEL ANGE 3 75794 Paris Francia Mostra sulla mappa Regione Ile-de-France Ile-de-France Paris Tipo di attività Research Organisations Contatto amministrativo Julie Zittel (Ms.) Ricercatore principale Artur Avila Cordeiro De Melo (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Francia Contributo UE € 1 020 840,00 Indirizzo RUE MICHEL ANGE 3 75794 Paris Mostra sulla mappa Regione Ile-de-France Ile-de-France Paris Tipo di attività Research Organisations Contatto amministrativo Julie Zittel (Ms.) Ricercatore principale Artur Avila Cordeiro De Melo (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato
