# Exponential Stability in the Perturbed Central Force Problem

@article{Bambusi2017ExponentialSI,
title={Exponential Stability in the Perturbed Central Force Problem},
author={Dario Bambusi and Alessandra Fus{\e} and M. Sansottera},
journal={Regular and Chaotic Dynamics},
year={2017},
volume={23},
pages={821-841}
}`
• Published 1 May 2017
• Mathematics
• Regular and Chaotic Dynamics
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…
3 Citations
• Mathematics
• 2022
We prove an abstract result giving a 〈t〉ǫ upper bound on the growth of the Sobolev norms of a time dependent Schrödinger equation of the form iψ̇ = H0ψ + V (t)ψ. H0 is assumed to be the Hamiltonian
• Mathematics
Communications in Mathematical Physics
• 2022
We study the asymptotic behavior of the spectrum of a quantum system which is a perturbation of a spherically symmetric anharmonic oscillator in dimension 2. We prove that a large part of its
• Mathematics
• 2020
We consider a 1D mechanical system $$\bar {\mathtt H}(\mathtt P,\mathtt Q)=\mathtt P^2+\bar {\mathtt G}(\mathtt Q)$$ in action-angle variable $(\mathtt P,\mathtt Q)$ where $\bar {\mathtt G}$ is a

## References

SHOWING 1-10 OF 28 REFERENCES

• Mathematics
• 2016
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
• Physics, Mathematics
• 2015
In this paper we study the dynamics of a soliton in the generalized NLS with a small external potential ϵV of Schwartz class. We prove that there exists an effective mechanical system describing the
• Mathematics, Physics
• 1993
We develop canonical perturbation theory for a physically interesting class of infinite-dimensional systems. We prove stability up to exponentially large times for dynamical situations characterized
• Physics, Mathematics
• 2003
We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger equations with an external potential. The equations have the feature that in the absence of the external
This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of
• Mathematics
• 1978
In this paper we shall show that the equations of motion of a solid, and also Liouville's method of integration of Hamiltonian systems, appear in a natural manner when we study the geometry of level
• Mathematics
• 1987
As in Part I of this paper, we consider the problem of the energy exchanges between two subsystems, of which one is a system of ν harmonic oscillators, while the other one is any dynamical system ofn
Abstract Many and important integrable Hamiltonian systems are ‘superintegrable’, in the sense that there is an open subset of their 2d-dimensional phase space in which all motions are linear on tori
• Physics
• 2014
We investigate the long-time stability in the neighborhood of the Cassini state in the conservative spin-orbit problem. Starting with an expansion of the Hamiltonian in the canonical Andoyer-Delaunay
• Physics
• 1987
The so-called problem of the realization of the holonomic constraints of classical mechanics is here revisited, in the light of Nekhoroshev-like classical perturbation theory. Precisely, if