Laboratoire de Physique Théorique
Toulouse - UMR 5152

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 : https://arxiv.org/abs/1804.11282.