Dario Bambusi

Universita' degli Studi di Milano


Bambusi D., Fusè A., Sansottera M.
Exponential Stability in the Perturbed Central Force Problem
2018, vol. 23, nos. 7-8, pp.  821-841
We consider the spatial central force problem with a real analytic potential. We prove that for all analytic potentials, but for the Keplerian and the harmonic ones, the Hamiltonian fulfills a nondegeneracy property needed for the applicability of Nekhoroshev’s theorem. We deduce stability of the actions over exponentially long times when the system is subject to an arbitrary analytic perturbation. The case where the central system is put in interaction with a slow system is also studied and stability over exponentially long time is proved.
Keywords: exponential stability, Nekhoroshev theory, perturbation theory, normal form theory, central force problem
Citation: Bambusi D., Fusè A., Sansottera M.,  Exponential Stability in the Perturbed Central Force Problem, Regular and Chaotic Dynamics, 2018, vol. 23, nos. 7-8, pp. 821-841
Bambusi D., Fusè A.
In this paper we prove a Nekhoroshev type theorem for perturbations of Hamiltonians describing a particle subject to the force due to a central potential. Precisely, we prove that under an explicit condition on the potential, the Hamiltonian of the central motion is quasiconvex. Thus, when it is perturbed, two actions (the modulus of the total angular momentum and the action of the reduced radial system) are approximately conserved for times which are exponentially long with the inverse of the perturbation parameter.
Keywords: Nekhoroshev theorem, central motion, Hamiltonian dynamics
Citation: Bambusi D., Fusè A.,  Nekhoroshev Theorem for Perturbations of the Central Motion, Regular and Chaotic Dynamics, 2017, vol. 22, no. 1, pp. 18-26

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