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This meeting is organised for Alain Chenciner's 60th birthday. Its main themes are Geometry, Dynamical Systems, the Calculus of variations and Celestial Mechanics in their widest sense, related to Analysis, Singularity Theory and applications.
Scientific committee: Jacques Laskar, John Mather, Harold Rosenberg, Carles Simò and Jean-Christophe Yoccoz.
Organisers: Alain Albouy, Daniel Bennequin, Marc Chaperon, Jacques Féjoz, Jacques Laskar et David Sauzin.
Announcement:
Alain Chenciner is a very active mathematician with an exceptionally broad range of interests. We shall restrict ourselves to problems he has been actively interested in.
The so-called KAM (Kolmogorov-Arnold-Moser) theorem states that nearly integrable Hamiltonian systems or symplectic maps have many invariant tori. However, these KAM tori do not fill the whole phase space, even locally. Our understanding of what happens elsewhere has increased notably in recent years by quite different methods : variational methods show that diffusion occurs generically, whereas specific examples exhibit the maximal diffusion speed compatible with Nekhoroshev's theorem. Variational methods also constitute the heart of the "weak KAM Theory", which includes the KAM tori in a family of more general compact invariant subsets.
Alain Chenciner has showed that such phenomena occur in families of general (non-symplectic) vector fields or diffeomorphisms. The general viewpoint was that of Singularity Theory &endash; Chenciner was very close to René Thom&endash; even though dynamical methods were needed. This work has opened the way to other interesting contributions by several authors.
In Celestial Mechanics, a fruitful collaboration between mathematicians and astronomers has lead to new results on old problems: determination of the central configurations in the N-body problem using algebraic methods and formal calculus, global study of the secular dynamics of planet systems via a refined version of KAM theory. The proof by Alain Chenciner and Richard Montgomery that there exists an astonishing periodic solution of the 3-body problem where the three bodies move along a "figure eight" curve has generated a lot of subsequent work, still in progress: numerical discovery of many more such "choregraphies" involving more and more bodies, extension of the variational methods and of the topological or symmetry constraints in order to give a rigorous mathematical proof that these phenomena do exist. Meanwhile, the description of the dynamics of the solar system has much benefited of the ideas of the mathematical theory of dynamical systems.
Speakers:
Alain Albouy (Paris), Yves Bouligand (Angers/Paris), Jean Bourgain (Princeton), Henk Broer (Groningen), Albert Fathi (Lyon), Jacques Féjoz (Paris), Gérard Iooss (Nice), Jacques Laskar (Paris), Patrice Le Calvez (Villetaneuse), Richard McGehee (Minneapolis), Christian Marchal (Paris), John Mather (Princeton), Richard Moeckel (Minneapolis), Richard Montgomery (Berkeley), Anatoly I. Neishtadt (Moscou), David Sauzin (Paris), Carles Simò (Barcelone), Bernard Teissier (Paris), Susanna Terracini (Milan), Dmitry Treschev (Moscou), Jean-Christophe Yoccoz (Paris).
Sponsors:
IHP - IHES - Observatoire de Paris - IMCCE - Institut de Mathématiques de Jussieu - UFR de Mathématiques de Paris VII - MJER.
contacts: laskar@imcce.fr, sauzin@imcce.fr, albouy@imcce.fr
Last revision (1/10/2003)
