Quasi-integrability in a class of systems generalizing the problem of two fixed centers

2002/10/09 by A. Albouy, Alain Albouy, Albouy, A. +2
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Chaotic Dynamics (nlin.CD) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #nlin.CD #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0210020

4, 14, typos added

arxiv created 2002/10/09 · openalex publication_date 2002/10/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of two fixed centers is a classical integrable problem, stated and integrated by Euler in 1760. The integrability is due to the unexpected first integral G. Some straightforward generalizations of the problem still have the generalization of G as a first integral, but do not possess the energy integral. We present some numerical integrations suggesting that in the domain of bounded orbits the behavior of these \it a priori non hamiltonian systems is very similar to the behavior of usual quasi-integrable systems.

Related

• Obstructions to Integrability of Nearly Integrable Dynamical Systems near Regular Level Sets
• Lectures on integrable Hamiltonian systems
• From Euler-Jacobi to Bogoyavlensky and back
• Two-center problem with harmonic-like interactions: periodic orbits and non-integrability
• A Non-Existence Result for Hamiltonian Integrators