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On the Existence of Drifting Orbits for Non-Convex Hamiltonian Systems
- Publication Year :
- 2015
-
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.<br />Comment: This paper has been withdrawn by the authors due to an important omission in the proof of Theorem 1.1
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1505.03969
- Document Type :
- Working Paper