A maximally superintegrable system on an -dimensional space of nonconstant curvature

2006/12/26 by Ángel Ballesteros, Angel Ballesteros, Alberto Enciso +3 · 5 citations
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP #msc:16W30 #msc:37J35 #msc:70H06 #nlin.SI

paper · pdf · doi:10.1016/j.physd.2007.09.021

published as PhysicaD237:505-509,2008 · 11 pages

arxiv created 2006/12/26 · openalex publication_date 2007/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

A novel Hamiltonian system in n dimensions which admits the maximal number 2n-1 of functionally independent, quadratic first integrals is presented. This system turns out to be the first example of a maximally superintegrable Hamiltonian on an n-dimensional Riemannian space of nonconstant curvature, and it can be interpreted as the intrinsic Smorodinsky-Winternitz system on such a space. Moreover, we provide three different complete sets of integrals in involution and solve the equations of motion in closed form.

Citations

• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Superintegrable systems in Darboux spaces
• Superintegrability in a two-dimensional space of nonconstant curvature

Cited by

• On Two Superintegrable Nonlinear Oscillators in N Dimensions
• Geometrical formulation of relativistic mechanics
• Global versus local superintegrability of nonlinear oscillators
• Quantum mechanics on spaces of nonconstant curvature: The oscillator problem and superintegrability
• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles