Are all classical superintegrable systems in two-dimensional space linearizable?
arXiv:1602.00705 · doi:10.1063/1.4974264
Abstract
Several examples of classical superintegrable systems in two-dimensional spac are shown to possess hidden symmetries leading to their linearization. They are those determined 50 years ago in [Phys. Lett. 13, 354 (1965)], and the more recent Tremblay-Turbiner-Winternitz system [J. Phys. A: Math. Theor. 42, 242001 (2009)]. We conjecture that all classical superintegrable systems in two-dimensional space have hidden symmetries that make them linearizable.
17 pages
References in corpus (7)
- Classical and Quantum Superintegrability with Applications
- Hidden Symmetries of Dynamics in Classical and Quantum Physics
- Hamiltonians separable in cartesian coordinates and third-order integrals of motion
- Reduction of superintegrable systems: the anisotropic harmonic oscillator
- Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform
- The classical Taub-Nut System: factorization, spectrum generating algebra and solution to the equations of motion
- Superintegrable systems in non-Euclidean plane: hidden symmetries leading to linearity