Obiettivo "The theme of the proposal is the mathematical investigation of chaos (in particular ergodic and spectral properties) in parabolic dynamics, via analytic, geometric and probabilistic techniques. Parabolic dynamical systems are mathematical models of the many phenomena which display a ""slow"" form of chaotic evolution, in the sense that nearby trajectories diverge polynomially in time. In contrast with the hyperbolic case and with the elliptic case, there is no general theory which describes parabolic dynamical systems. Only few classical examples are well understood.The research plan aims at bridging this gap, by studying new classes of parabolic systems and unexplored properties of classical ones. More precisely, I propose to study parabolic flows beyond the algebraic set-up and infinite measure-preserving parabolic systems, both of which are very virgin fields of research, and to attack open conjectures and questions on fine chaotic properties, such as spectra and rigidity, for area-preserving flows. Moreover, connections between parabolic dynamics and respectively number theory, mathematical physics and probability will be explored. g New techniques, stemming from some recent breakthroughs in Teichmueller dynamics, spectral theory and infinite ergodic theory, will be developed.The proposed research will bring our knowledge significantly beyond the current state-of-the art, both in breadth and depth and will identify common features and mechanisms for chaos in parabolic systems. Understanding similar features and common geometric mechanisms responsible for mixing, rigidity and spectral properties of parabolic systems will provide important insight towards an universal theory of parabolic dynamics." Campo scientifico natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicsapplied mathematicsmathematical model 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-2013-StG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-SG - ERC Starting Grant Istituzione ospitante UNIVERSITAT ZURICH Contributo UE € 373 362,59 Indirizzo RAMISTRASSE 71 8006 Zurich Svizzera Mostra sulla mappa Regione Schweiz/Suisse/Svizzera Zürich Zürich Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Corinna Ulcigrai (Dr.) Contatto amministrativo Sofia Karakostas (Ms.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (2) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto UNIVERSITAT ZURICH Svizzera Contributo UE € 373 362,59 Indirizzo RAMISTRASSE 71 8006 Zurich Mostra sulla mappa Regione Schweiz/Suisse/Svizzera Zürich Zürich Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Corinna Ulcigrai (Dr.) Contatto amministrativo Sofia Karakostas (Ms.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato UNIVERSITY OF BRISTOL Regno Unito Contributo UE € 820 171,41 Indirizzo BEACON HOUSE QUEENS ROAD BS8 1QU Bristol Mostra sulla mappa Regione South West (England) Gloucestershire, Wiltshire and Bristol/Bath area Bristol, City of Tipo di attività Higher or Secondary Education Establishments Contatto amministrativo Audrey Michael (Mrs.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato