We extend the Poincaré--Birkhoff Theorem to a Hamiltonian system which couples two systems with fairly different behaviors; the first one involves a twist assumption, while the second one is generated from a nonresonant isochronous center. By a suitable change of variables we modify the second system into a perturbation of a nonresonant linear one, and then prove that there exist multiple periodic solutions.

Periodic solutions of Hamiltonian systems coupling twist with an isochronous center

Fonda, Alessandro
;
Ullah, Wahid
2024-01-01

Abstract

We extend the Poincaré--Birkhoff Theorem to a Hamiltonian system which couples two systems with fairly different behaviors; the first one involves a twist assumption, while the second one is generated from a nonresonant isochronous center. By a suitable change of variables we modify the second system into a perturbation of a nonresonant linear one, and then prove that there exist multiple periodic solutions.
2024
4-dic-2023
Pubblicato
https://projecteuclid.org/journals/differential-and-integral-equations/volume-37/issue-5_2f_6/Periodic-solutions-of-Hamiltonian-systems-coupling-twist-with-an-isochronous/10.57262/die037-0506-323.short
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3068461
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