2010/11/02 by A Ballesteros, Angel Ballesteros, A Enciso +7 · 1 citation
Mathematics · Physics and Astronomy · #Frenet–Serret formulas #Hamiltonian (control theory) #Hamiltonian system #Kepler problem #Noncommutative and Quantum Gravity Theories #Nonlinear Waves and Solitons #Quantization (signal processing) #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/1742-6596/284/1/012011
published as J.Phys.Conf.Ser.284:012011,2011 · 13 pages; based in the contribution to the 28th International Colloquium on Group Theoretical Methods in Physics, Northumbria University (U.K.), 26-30th July 2010
arxiv created 2010/11/02 · openalex publication_date 2011/03/01 · arxiv updated 2011/04/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of Hamiltonian systems defined on certain 3-dimensional (Riemannian) spaces. These two systems are shown to be either the Kepler or the oscillator potentials on the corresponding Bertrand spaces, and both of them are maximally superintegrable. Afterwards, the relationship between such Bertrand Hamiltonians and position-dependent mass systems is explicitly established. These results are illustrated through the example of a superintegrable (nonlinear) oscillator on a Bertrand-Darboux space, whose quantization and physical features are also briefly addressed.