Workshop on Mathematical Aspects of Celestial Mechanics

Paris, Institut Henri Poincaré (amphi Darboux), December 11-20, 2007

Schedule

Mornings are devoted to 4-session courses. Afternoons consist of special sessions, usually starting at 2:30 pm. A special room at IHP will be devoted to posters.

Examples of Arnold diffusion
Organizers: V. Kaloshin & M. Levi
Tuesday 11 9:30 - 10:45 am M.-C. Arnaud, Green's fiber bundles: a dynamical study
11 am - 12:15 n G. Contreras, Genericity of positive entropy for geodesic flows
Organizers: M. Chaperon & C. Viterbo
2:30 pm P. Le Calvez, About the linking number of periodic points of a plane homeomorphism
3:45 pm M. Chaperon, Birth control in generalized Hopf bifurcations
5 pm S. Kuksin, Perturbations of integrable Hamiltonian PDE
Wednesday 12 9:30 - 10:45 am M.-C. Arnaud
11 am - 12:15 n G. Contreras
2:30 - 5 pm Trip towards real planets and asteroids
Organizers: L. Niederman & P. Robutel
U. Locatelli, Explicit construction of KAM tori in celestial mechanics
H. Skokos, Realistic estimations of the stability region of the Trojan asteroids
J. Laskar (presenting the work of P. Robutel), Numerical investigation of the Trojan dynamics –stability, resonance overlapping and diffusion
Thursday 13 9:30 - 10:45 am M.-C. Arnaud
11 am - 12:15 n G. Contreras
The n-body problem
Organizers: A. Albouy & R. Moeckel
2:30 pm S. Bolotin, Second species solutions of the three-body problem
3:45 pm K.-C. Chen, On the action minimizing retrograde solutions of the three-body problem
Friday 14 9:30 - 10:45 am M.-C. Arnaud
11 am - 12:15 n G. Contreras
Dynamical Systems Seminar
Organizers: H. Eliasson & J.-C. Yoccoz
2:30 pm L. Chierchia, Spin-orbit resonances in the Solar system: periodic and quasi-periodic attractors in the small dissipation limit
3:45 pm K. Pakdaman, Neuronal coding
5 pm V. Kaloshin, Hausdorff dimension of oscillatory motions for the 3 body problem
Saturday 15 at Observatoire
(Talks in Salle du Conseil)
History of Celestial Mechanics
10:30 am C.-M. Marle, Deux Mémoires de Lagrange et de Poisson sur la méthode de la variation de la constante
11:15 am J. Laskar, Lagrange and the stability of the solar system
12 n F. Brechenmacher, Sur l'équation à l'aide de laquelle on détermine les inégalités séculaires (1766–1874)
12:30 n Cold lunch in the restaurant of Bâtiment B
2 pm Visit of Observatoire
by J. Souchay, Observatoire de Paris
Featured session
3:30 pm C. Simó, Towards a global study of Area Preserving Maps. Applications to the stability around L4,5 in the restricted three-body problem
4:30 pm D. Treschev, Polymorphisms and adiabatic chaos
Sunday 16 Free
Monday 17 9:30 - 10:45 am R. Moeckel, Topics on the three-body problem
11 am - 12:15 n A. Neishtadt, Adiabatic invariants
Small denominators
2:30 pm B. Fayad, Wandering tori in the exterior billard around the half-disc
3:45 pm R. Krikorian, Généralisation du théorème de Dinaburg-Sinai et théorie KAM-Liouville
6 pm - 8 pm
8 pm - 10 pm
(two groups)
Astronomical observation
conducted by F. Sèvres
Tuesday 18 9:30 - 10:45 am R. Moeckel
11 am - 12:15 n A. Neishtadt
Weak KAM theory and variational methods
Organizers: P. Bernard & A. Fathi
2:30 pm L. Rifford, On the quotient Aubry set
3:45 pm A. Abbondandolo, High action orbits of Hamiltonian systems and their asymptotic Maslov index
5 pm A. Venturelli, Globally minimizing parabolic solutions in the Newtonian N-body problem
Wednesday 19 9:30 - 10:45 am R. Moeckel
11 am - 12:15 n A. Neishtadt
2:30 pm M. Levi, Geometry of Arnold diffusion
3:45 pm V. Kaloshin, Arnold diffusion through a double resonance and applications
5 pm Informal discussion
6 pm - 8 pm
8 pm - 10 pm
(two groups)
Astronomical observation
conducted by F. Sèvres (up to confirmation)
Thursday 20 9:30 - 10:45 am R. Moeckel
11 am - 12:15 n A. Neishtadt
Collisions and Topology
Organizers: A. Chenciner & R. Montgomery
2:30 pm S. Terracini, Singularities and collisions of generalized solutions to the N-body problem
3:45 pm V. Kaloshin, Arnold diffusion along nearly parabolic orbits for the restricted planar 3-body problem