On the Existence of Drifting Orbits for Non-Convex Hamiltonian Systems

Borislav Yordanov; Roumyana Yordanova

On the Existence of Drifting Orbits for Non-Convex Hamiltonian Systems

Classical Analysis and ODEs 2015-06-19 v2 Dynamical Systems

Authors: Borislav Yordanov , Roumyana Yordanova

Abstract

We show the existence of drifting orbits for certain perturbations of non-convex Hamiltonian systems with several degrees of freedom. These orbits remain in the vicinity of resonant surfaces where the action variables can undergo changes $O(1)$ infinitely often although the size of perturbations $O(\epsilon)$ can be arbitrarily small. The first drifts occur in a period of time $O(1/\epsilon)$ and then reoccur with frequencies independent of $\epsilon$ . We also perform numerical simulations to compare the effects of two conditions for instability in two four-dimensional examples with random parameters.

Keywords

non-convex hamiltonian systems drifting orbits perturbations resonant surfaces action variables numerical simulations instability conditions

Cite

@article{arxiv.1505.03969,
  title  = {On the Existence of Drifting Orbits for Non-Convex Hamiltonian Systems},
  author = {Borislav Yordanov and Roumyana Yordanova},
  journal= {arXiv preprint arXiv:1505.03969},
  year   = {2015}
}

Comments

This paper has been withdrawn by the authors due to an important omission in the proof of Theorem 1.1

On the Existence of Drifting Orbits for Non-Convex Hamiltonian Systems

Abstract

Keywords

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