2018/10/31 by A. V. Tsiganov
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Algebraic number #Classical mechanics #Elliptic integral #Harmonic function #Harmonic oscillator #Kepler #Kepler problem #Mathematical analysis #Mathematical physics #Mathematics #Motion (physics) #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #math-ph #math.DS #math.MP #nlin.SI
paper · pdf · doi:10.1088/1402-4896/ab0297
17 pages, 3 figures, LaTeX with Amsfonts, with corrected misprints
openalex publication_date 2019/01/29 · arxiv created 2019/02/14 · arxiv updated 2019/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract The harmonic oscillator and the Kepler problem are superintegrable systems which admit more integrals of motion than degrees of freedom and all these integrals are polynomials in momenta. We present superintegrable deformations of the oscillator and the Kepler problem with algebraic and rational first integrals. Also, we discuss a family of superintegrable metrics on the two-dimensional sphere, which have similar first integrals.