Hovering Sets in Near Pseudo-Integrable Hamiltonian Impact Systems
Chaotic Dynamics
2025-09-30 v1 Dynamical Systems
Abstract
The transition from rotational to discontinuous behavior of the return map of the perturbed oscillators-step system, a paradigm model for a perturbation of a pseudo-integrable Hamiltonian impact system, is studied. The form of the return map is derived, and a truncated form of this map is simulated and analyzed. For a set of parameters the existence of a hovering set, a set of non-resonant orbits that pass sometimes above the step and sometimes to its side, without ever impacting it, is established and quantified. Its destruction as the sign of the perturbation term is reversed is established.
Keywords
Cite
@article{arxiv.2509.24688,
title = {Hovering Sets in Near Pseudo-Integrable Hamiltonian Impact Systems},
author = {Idan Pazi and Alexandra Zobova and Vered Rom-Kedar},
journal= {arXiv preprint arXiv:2509.24688},
year = {2025}
}