2015/01/06 by Manuel F. Rañada, Ranada, Manuel F.
Physics and Astronomy · #37J35 #70H06 #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1501.01258
openalex publication_date 2015/01/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The properties of the Tremblay-Turbiner-Winternitz system (related to the harmonic oscillator) were recently studied on the two-dimensional spherical Sκ2 (κ>0) and hiperbolic Hκ2 (κ<0) spaces (J. Phys. A : Math. Theor. 47, 165203, 2014). In particular, it was proved the higher-order superintegrability of the TTW system by making use of (i) a curvature-dependent formalism, and (ii) existence of a complex factorization for the additional constant of motion. Now a similar study is presented for the Post-Winternitz system (related to the Kepler problem). The curvature κ is considered as a parameter and all the results are formulated in explicit dependence of κ. This technique leads to a correct definition of the Post-Winternitz (PW) system on spaces with curvature κ, to a proof of the existence of higher-order superintegrability (in both cases, κ>0 and κ<0), and to the explicit expression of the constants of motion.