Cel "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)." Dziedzina nauki natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesmathematicsapplied mathematicsdynamical systems Słowa kluczowe ergodic theory correlation functions zeta functions linear response billiards nonuniformly hyperbolic systems transfer operators Program(-y) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Temat(-y) ERC-2017-ADG - ERC Advanced Grant Zaproszenie do składania wniosków ERC-2017-ADG Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-ADG - Advanced Grant Instytucja przyjmująca CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Wkład UE netto € 1 830 070,00 Adres RUE MICHEL ANGE 3 75794 Paris Francja Zobacz na mapie Region Ile-de-France Ile-de-France Paris Rodzaj działalności Research Organisations Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 1 830 070,00 Beneficjenci (1) Sortuj alfabetycznie Sortuj według wkładu UE netto Rozwiń wszystko Zwiń wszystko CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Francja Wkład UE netto € 1 830 070,00 Adres RUE MICHEL ANGE 3 75794 Paris Zobacz na mapie Region Ile-de-France Ile-de-France Paris Rodzaj działalności Research Organisations Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 1 830 070,00
