Work

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

Year: 2025

Type: article

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.

Source: Chaos An Interdisciplinary Journal of Nonlinear Science

DOI: 10.1063/5.0274284

Authors: A. M. Escobar Ruiz, Lidia Jiménez-Lara, J. Llibre, Marco A. Zurita

Institutions: Universidad Autónoma Metropolitana, Universitat Autònoma de Barcelona

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green