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arXiv · 1505.03969

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

Borislav Yordanov·Roumyana Yordanova
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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.

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Borislav Yordanov, Roumyana Yordanova. 2015-05-15. On the Existence of Drifting Orbits for Non-Convex Hamiltonian Systems. https://arxiv.org/abs/1505.03969

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