Non-Integrability of a weakly integrable Hamiltonian system
arXiv:nlin/0308033 · doi:10.1023/B:CELE.0000016820.95989.ff
Abstract
The geometric approach to mechanics based on the Jacobi metric allows to easily construct natural mechanical systems which are integrable (actually separable) at a fixed value of the energy. The aim of the present paper is to investigate the dynamics of a simple prototype system outside the zero-energy hypersurface. We find that the general situation is that in which integrability is not preserved at arbitrary values of the energy. The structure of the Hamiltonian in the separating coordinates at zero energy allows a perturbation treatment of this system at energies slightly different from zero, by which we obtain an analytical proof of non-integrability.
24 pages, accepted for publication on Celestial Mechanics and Dynamical Astronomy
References in corpus (4)
- A unified treatment of quartic invariants at fixed and arbitrary energy
- A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta
- Invariants at fixed and arbitrary energy. A unified geometric approach
- On the Global Dynamics of the Anisotropic Manev Problem