Ecole d'été du trimestre Mathematical Methods for Celestial Mechanics

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La FSMP finance les séjours de ses étudiants

La FSMP prendra en charge les frais de transport, de repas et d'hébergement pour les doctorants des laboratoires de son réseau désirant participer à l'école d'été préparatoire au trimestre IHP intitulé Mathematical Methods for Celestial Mechanics (du 16 septembre au 14 décembre 2013 à l'IHP).

Cette école d'été aura lieu au CIRM.

Pour bénéficier de ce financement, envoyez un CV à l'organisateur :Pr. Jerome Perez ( avant le 26 avril 2013.

Attention, il y a un numerus clausus !

Pour en savoir plus sur le trimestre et sur l'école d'été, consultez le site

Sujet et objectif de l'école d'été

For centuries, the N-body problem of Celestial Mechanics has challenged many generation of mathematicians.

Not only it represents an historical milestone of Mathematics, but it is paradigmatic of any complex system of interacting particles. In its full generality, it can be neither solved nor simpli ed in a signi cant way.

As a dynamical system, it has the fascinating feature of hosting regular and chaotic regimes and has often inspired the elaboration of new mathematical theories of local, perturbative and global nature. Indeed, to be attacked e ciently, it requires a sophisticated mixture of algebraic, analytical, geometrical, topological and probabilistic techniques. Recent developments have regarded work by Chierchia and Pinzari (Inv. math, to appear), Chenciner and Mongomery (Ann. of Math., 2000), Ferrario and Terracini (Inv. math., 2004), Chen (Ann. of Math, 2010), Gronchi, Fusco, and Negrini (Inv. math., 2011), Hampton and Moeckel (Inv. math., 2006), Albouy and Kaloshin (Ann. of Math., to appear), to mention only a few of the best papers. Our aim is to bring together the main specialists on the N-body problem together with the leaders of different areas in dynamical systems (variational methods, Aubrey-Mather theory, Hamiltonian dynamics, ergodic theory) trying to build a theoretical framework suitable to attack some of the many unsolved aspects of the N-body problem. Gathering together the proposed participants will be extremely helpful in undertaking the following directions: coexistence of stable and unstable regions; analysis of mean-orbital resonances; Nekhoroshev analysis of the secular approximate invariants (mutual inclinations and eccentricities); long-period periodic orbits near invariant tori; intermediate stable/unstable invariant tori; resonant tori; instabilities (including special instances of Arnold di usion), possible applications of AubryMather theory study of bounded and parabolic orbits; possible applications of weak KAM theory to the N-body problem; stability of periodic trajectories found by variational methods; and regularization of collisions