HAMPDES

Hamiltonian PDE's and small divisor problems: a dynamical systems approach

Coordinatore	UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Italy [IT]
Totale costo	678˙000 €
EC contributo	678˙000 €
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-2012-StG_20111012
Funding Scheme	ERC-SG
Anno di inizio	2012
Periodo (anno-mese-giorno)	2012-11-01   -   2017-10-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITA DEGLI STUDI DI NAPOLI FEDERICO II.  Organization address address: Corso Umberto I 40 city: NAPOLI postcode: 80138 contact info Titolo: Ms. Nome: Immacolata Cognome: Diez Email: send email Telefono: +39 81 65720	IT (NAPOLI)	beneficiary	279˙600.00
2	UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA  Organization address address: Piazzale Aldo Moro 5 city: ROMA postcode: 185 contact info Titolo: Dr. Nome: Michela Cognome: Procesi Email: send email Telefono: +39 6 49913249	IT (ROMA)	hostInstitution	398˙400.00
3	UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA  Organization address address: Piazzale Aldo Moro 5 city: ROMA postcode: 185 contact info Titolo: Ms. Nome: Maria Rita Cognome: Ullucci Email: send email Telefono: +39 6 49923273 Fax: +39 6 49913275	IT (ROMA)	hostInstitution	398˙400.00

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 Obiettivo del progetto (Objective)

'A large number of partial differential equations of Physics have the structure of an infinite-dimensional Hamiltonian dynamical system. In this class of equations appear, among others, the Schrödinger equation (NLS), the wave equation (NLW), the Euler equations of hydrodynamics and the numerous models that derive from it. The study of these equations poses some fundamental questions that have inspired an entire research field in the last twenty years: the investigation of the main invariant structures of the phase space of a Hamiltonian system, starting from its stationary, periodic and quasi-periodic orbits. As in the case of finite-dimensional dynamical systems, one of the main problems in this field is linked to the well-known 'small divisors problem'. A further difficulty is due to the fact that 'physically' interesting equations, without outer parameters, are typically resonant and/or contain derivatives in the non-linearity. There are many fundamental open questions in this field. Our main goals are 1) the study of quasi-periodic solutions, in particular for semi-linear and quasi-linear equations. 2)Study of normal forms, both in integrable and non-integrable cases. 3) Applications to hydrodynamics and search of quasi-periodic solutions in water wave problems.4) Study of almost periodic solutions for nonlinear PDEs. 5) quasi-periodic solutions for resonant systems with minimal restrictions on the non-linearity. Together with my group in Naples we already have developed several techniques to approach these problems and we have several ideas of possible innovative approaches, combining Nash-Moser and KAM methods, Normal Form Theory, Para-differential calculus, combinatorial methods.'