Periodic orbits in a Hamiltonian system of stellar type

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2024-06-20 DOI:10.1016/j.physd.2024.134261

Jhon Vidarte , Yrina Vera-Damián , Walter Gonzales

引用次数: 0

Abstract

We investigate the existence of periodic orbits in a perturbed Hamiltonian system of stellar type in 1:1 resonance. The perturbation consists of a potential of degree four with two real parameters. We determine six families of periodic orbits using reduction and averaging theories. Also, we characterize the stability of these orbits and their bifurcation curves in terms of the parameters. Finally, we show a complete picture of the choreographies of critical points originating the periodic orbits.

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恒星型哈密顿系统中的周期轨道

我们研究了在 1:1 共振的恒星型扰动哈密顿系统中是否存在周期性轨道。扰动由一个具有两个实参数的四度势组成。我们利用还原和平均理论确定了六个周期轨道族。此外，我们还根据参数描述了这些轨道及其分岔曲线的稳定性。最后，我们展示了周期轨道临界点编排的全貌。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.