English

A remark on the onset of resonance overlap

Dynamical Systems 2023-08-30 v1

Abstract

Chirikov's celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigourous. We introduce two simple Hamiltonian systems, each depending on two parameters measuring respectively the distance to resonance overlap and non-integrability. Within some thin region of the parameter plane, classical perturbation theory shows the existence of global instability and symbolic dynamics, thus illustrating Chirikov's criterion.

Keywords

Cite

@article{arxiv.2308.15222,
  title  = {A remark on the onset of resonance overlap},
  author = {Jacques Fejoz and Marcel Guardia},
  journal= {arXiv preprint arXiv:2308.15222},
  year   = {2023}
}