000077270 001__ 77270 000077270 005__ 20190226082308.0 000077270 0247_ $$2doi$$a10.1088/1751-8113/47/16/165203 000077270 0248_ $$2sideral$$a108594 000077270 037__ $$aART-2014-108594 000077270 041__ $$aeng 000077270 100__ $$aRañada, M. F. 000077270 245__ $$aThe Temblay-Turbiner-Winternitz system on spherical and hyperbolic spaces 000077270 260__ $$c2014 000077270 5060_ $$aAccess copy available to the general public$$fUnrestricted 000077270 5203_ $$aThe higher-order superintegrability of the Tremblay-Turbiner-Winternitz system (related to the harmonic oscillator) is studied on the two-dimensional spherical and hiperbolic spaces, S¿2 (¿ > 0), and H¿2 (¿ < 0). The curvature ¿ is considered as a parameter and all the results are formulated in explicit dependence of ¿. The idea is that the additional constant of motion can be factorized as the product of powers of two particular rather simple complex functions (here denoted by Mr and Nf). This technique leads to a proof of the superintegrability of the Tremblay-Turbiner-Winternitz system on S¿2 (¿ > 0) and H¿2 (¿ < 0), and to the explicit expression of the constants of motion. 000077270 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-1$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2012-33575 000077270 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000077270 590__ $$a1.583$$b2014 000077270 591__ $$aPHYSICS, MULTIDISCIPLINARY$$b31 / 78 = 0.397$$c2014$$dQ2$$eT2 000077270 591__ $$aPHYSICS, MATHEMATICAL$$b16 / 54 = 0.296$$c2014$$dQ2$$eT1 000077270 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000077270 773__ $$g47, 16 (2014), 165203 (9pp)$$pJournal of Physics A-Mathematical and Theoretical$$tJournal of Physics A-Mathematical and Theoretical$$x1751-8113 000077270 8564_ $$s333819$$uhttps://zaguan.unizar.es/record/77270/files/texto_completo.pdf$$yPostprint 000077270 8564_ $$s43918$$uhttps://zaguan.unizar.es/record/77270/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000077270 909CO $$ooai:zaguan.unizar.es:77270$$particulos$$pdriver 000077270 951__ $$a2019-02-26-08:06:16 000077270 980__ $$aARTICLE