Objective 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. Fields of science 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) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2010-StG_20091028 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS EU contribution € 1 020 840,00 Address RUE MICHEL ANGE 3 75794 Paris France See on map Region Ile-de-France Ile-de-France Paris Activity type Research Organisations Administrative Contact Julie Zittel (Ms.) Principal investigator Artur Avila Cordeiro De Melo (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS France EU contribution € 1 020 840,00 Address RUE MICHEL ANGE 3 75794 Paris See on map Region Ile-de-France Ile-de-France Paris Activity type Research Organisations Administrative Contact Julie Zittel (Ms.) Principal investigator Artur Avila Cordeiro De Melo (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
