Marco Sansottera (University of Milan)

Title: Quasi-convexity of the Hamiltonian for non Harmonic or non Keplerian
central potentials.

Abstract:

We consider the planar central motion with a real analytic potential. We
prove that the corresponding Hamiltonian, when written in action angle
variables, is almost everywhere quasiconvex, the only exceptions being
the Keplerian and the Harmonic potentials. We deduce persistence of most
KAM tori for the perturbed planar system. We also deduce a Nekhoroshev
type stability result for the perturbed spatial central motion. Such a
latter result covers also the case where the central system is put in
interaction with a slow system.