A geometric approach to the separability of the Neumann-Rosochatius system

2003/07/12 by Claudio Bartocci, Bartocci, Claudio, Gregorio Falqui +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.DG #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0307021

LaTeX file, 14 pages

arxiv created 2003/07/12 · openalex publication_date 2003/07/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.

Cited by

• Simultaneous separation for the Neumann and Chaplygin systems

Related

• Bi-Hamiltonian aspects of the separability of the Neumann system
• Separable bi-Hamiltonian systems with quadratic in momenta first integrals
• Separation of variables for bi-Hamiltonian systems
• Geodesic flows for the Neumann-Rosochatius systems
• Geometrical Theory of Separation of Variables, a review of recent developments