Two-center problem with harmonic-like interactions: periodic orbits and non-integrability

2024/05/23 by A. M. Escobar-Ruiz, Lidia Jiménez–Lara, Ruiz, A. M. Escobar +4
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Physical sciences #Material Science and Thermodynamics #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2405.15048

openalex publication_date 2024/05/23 · openalex created_date 2024/05/28 · openalex updated_date 2026/07/28

Abstract

We study the classical planar two-center problem of a particle m subjected to harmonic-like interactions with two fixed centers. For convenient values of the dimensionless parameter of this problem we use the averaging theory for showing analytically the existence of periodic orbits bifurcating from two of the three equilibrium points of the Hamiltonian system modeling this problem. Moreover, it is shown that the system is generically non-integrable in the sense of Liouville-Arnold. The analytical results are complemented by numerical computations of the Poincaré sections and Lyapunov exponents. Explicit periodic orbits bifurcating from the equilibrium points are presented as well.

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