Obiettivo "The ergodic theory of smooth dynamical systems enjoying some form of hyperbolicity has undergone important progress since the beginning of the twenty first century, in part due to the development of a new technical tool: anisotropic Banach or Hilbert spaces, on which transfer operators have good spectral properties. Very recently, such tools have yielded exponential mixing for dispersing (Sinai) billiard flows (i.e. the 2D periodic Lorentz gas), which are the archetypal smooth systems with singularities. We will study other challenging natural systems, mostly with singularities, by using functional analytical tools, in particular transfer operators acting on anisotropic spaces (including the new ""ultimate'"" space introduced recently, which combines desirable features of several existing spaces), and revisiting the Milnor-Thurston kneading theory to obtain nuclear decompositions in low regularity. Goals of the project include:-Thermodynamic formalism for the Sinai billiard maps and flows (2D periodic Lorentz gas), in particular existence and statistical properties of the measure of maximal entropy.-Intrinsic resonances of Sinai billiard maps and flows (2D periodic Lorentz gas) via the dynamical zeta function.-Fine statistical properties of (infinite measure) semi-dispersing billiards with non compact cusps.-Growth of dynamical determinants and zeta functions of differentiable (non analytic) geodesic flows, with applications to the global Gutzwiller formula.-Fractional response and fractional susceptibility function for transversal families of smooth nonuniformly hyperbolic maps (including the logistic family)." Campo scientifico natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesmathematicsapplied mathematicsdynamical systems Parole chiave ergodic theory correlation functions zeta functions linear response billiards nonuniformly hyperbolic systems transfer operators Programma(i) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Argomento(i) ERC-2017-ADG - ERC Advanced Grant Invito a presentare proposte ERC-2017-ADG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-ADG - Advanced Grant Istituzione ospitante CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Contribution nette de l'UE € 1 830 070,00 Indirizzo RUE MICHEL ANGE 3 75794 Paris Francia Mostra sulla mappa Regione Ile-de-France Ile-de-France Paris Tipo di attività Research Organisations Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 830 070,00 Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo netto dell'UE Espandi tutto Riduci tutto CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Francia Contribution nette de l'UE € 1 830 070,00 Indirizzo RUE MICHEL ANGE 3 75794 Paris Mostra sulla mappa Regione Ile-de-France Ile-de-France Paris Tipo di attività Research Organisations Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 830 070,00
