Year: 2026
Type: article
Abstract: . The transition from rotational to discontinuous behavior of the return map of the perturbed oscillator-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 model of this map is simulated and analyzed. For a set of parameters the existence of a hovering set, a set of nonresonant orbits that pass sometimes above the step and sometimes to its side, without ever impacting it, is established and quantified. It is further shown that reversing the sign of the perturbation destroys this set.
DOI: 10.1137/25m1804285
Authors: Idan Pazi, Alexandra Zobova, Vered Rom-Kedar
Institutions: Weizmann Institute of Science, Tel Aviv University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Award: G2223676658
OpenAlex ID: W4415337147
FWCI:
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