On potentials whose level sets are orbits
Event details
| Date | 22.11.2024 |
| Hour | 14:15 |
| Speaker | Prof. Philippe Bolle (University of Avignon - France) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract
A level orbit of a mechanical Hamiltonian system is a solution of the equation of motion that is contained in a level set of the potential energy. In this talk we shall answer the following question : what can be said about smooth potential energy functions on the plane such that any point of the plane lies on a level orbit? We call such functions Levi potentials. We shall see that if a Levi potential is analytic, then it is necessarily radial. However any convex compact subset of the plane is the critical set of a Levi potential. The proof of these results relies on the properties of the inverse curvature flow.
This is a joint work with M. Mazzuchelli and A. Venturelli.
A level orbit of a mechanical Hamiltonian system is a solution of the equation of motion that is contained in a level set of the potential energy. In this talk we shall answer the following question : what can be said about smooth potential energy functions on the plane such that any point of the plane lies on a level orbit? We call such functions Levi potentials. We shall see that if a Levi potential is analytic, then it is necessarily radial. However any convex compact subset of the plane is the critical set of a Levi potential. The proof of these results relies on the properties of the inverse curvature flow.
This is a joint work with M. Mazzuchelli and A. Venturelli.
Practical information
- Informed public
- Free
Contact
- B. Buffoni, SMA