Exponential Stability in the Perturbed Central Force Problem

  title={Exponential Stability in the Perturbed Central Force Problem},
  author={Dario Bambusi and Alessandra Fus{\`e} and M. Sansottera},
  journal={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… 

Growth of Sobolev norms in quasi integrable quantum systems

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

On the Stable Eigenvalues of Perturbed Anharmonic Oscillators in Dimension Two

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

Action-angle Variables for Generic 1D Mechanical Systems.

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



Nekhoroshev theorem for perturbations of the central motion

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

Freezing of Energy of a Soliton in an External Potential

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

Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems

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

Solitary Wave Dynamics in an External Potential

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

Hamiltonian perturbation theory on a manifold

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

Generalized Liouville method of integration of Hamiltonian systems

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

Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II

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

Superintegrable Hamiltonian Systems: Geometry and Perturbations

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

Effective stability around the Cassini state in the spin-orbit problem

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

Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part I

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