Sur ce site

Sur le Web du CNRS

Accueil du site > Séminaires > Séminaires 2018 > Isochrony and self-gravitating system dynamics

Mardi 26 juin 2018 - 14:00

Isochrony and self-gravitating system dynamics

Alicia Simon-Petit (ENSTA ParisTech & l’Ecole Polytechnique)

par Revaz Ramazashvili - 26 juin 2018

In the potential theory, isochrony has been introduced by Michel Hénon in 1959 to characterize astrophysical observations of some globular clusters. Today, Michel Hénon’s isochrone potential is mainly used for his integrable property in numerical simulations, but is generally not really known. The talk aims at presenting new results on isochrony that have particular importance in self-gravitating dynamics.

After introducing Michel Hénon’s isochrone definition, based on a brilliant remark on the gravitational dynamics, we will complete the set of isochrone potentials. This completeness will allow us to exhibit a particular relation between the isochrones by generalizing the Bohlin transformation. In fact, we will determine the keplerian nature of isochrones that is at the heart of the new isochrone relativity. Eventually, the consequences of this relativity in celestial mechanics (generalization of Kepler’s Third law, Bertrand’s theorem) will be applied to analyze the result of a gravitational collapse.

References :

Hénon M., L’amas isochrone, Annales d’Astrophysique,

Vol. 22, p.126, 1959

Simon-Petit A., Perez J., Duval G., Isochrony in 3D radial potentials, Comm. in Math. Phys., Accepted. Preprint :

Post-scriptum :

contact : P.-H. Chavanis