QUASIPERIODIC

Dynamics of quasiperiodic type

 Coordinatore CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE 

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 Nazionalità Coordinatore France [FR]
 Totale costo 1˙020˙840 €
 EC contributo 1˙020˙840 €
 Programma 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)
 Code Call ERC-2010-StG_20091028
 Funding Scheme ERC-SG
 Anno di inizio 2010
 Periodo (anno-mese-giorno) 2010-12-01   -   2015-11-30

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

 Organization address address: Rue Michel -Ange 3
city: PARIS
postcode: 75794

contact info
Titolo: Dr.
Nome: Artur
Cognome: Avila Cordeiro De Melo
Email: send email
Telefono: +33 1 44278556
Fax: +33 1 44277852

FR (PARIS) hostInstitution 1˙020˙840.00
2    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

 Organization address address: Rue Michel -Ange 3
city: PARIS
postcode: 75794

contact info
Titolo: Ms.
Nome: Julie
Cognome: Zittel
Email: send email
Telefono: +33 1 42349416
Fax: +33 1 42349508

FR (PARIS) hostInstitution 1˙020˙840.00

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

spectral    flows    global    translation    consists    cocycles    class    certain    typical    dependence    dynamics    theory    small    potentials    had    billiards    quasiperiodic    techniques   

 Obiettivo del progetto (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.'

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