000118159 001__ 118159
000118159 005__ 20230519145553.0
000118159 0247_ $$2doi$$a10.3934/jgm.2021003
000118159 0248_ $$2sideral$$a126325
000118159 037__ $$aART-2021-126325
000118159 041__ $$aeng
000118159 100__ $$0(orcid)0000-0002-8402-2332$$aFernández Rañada, M.$$uUniversidad de Zaragoza
000118159 245__ $$aQuasi-bi-Hamiltonian structures and superintegrability: Study of a Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion
000118159 260__ $$c2021
000118159 5060_ $$aAccess copy available to the general public$$fUnrestricted
000118159 5203_ $$aThe existence of quasi-bi-Hamiltonian structures for a two-dimensional superintegrable (k(1), k(2), k(3))-dependent Kepler-related problem is studied. We make use of an approach that is related with the existence of some complex functions which satisfy interesting Poisson bracket relations and that was previously applied to the standard Kepler problem as well as to some particular superintegrable systems as the Smorodinsky-Winternitz (SW) system, the Tremblay-Turbiner-Winternitz (TTW) and Post-Winternitz (PW) systems. We prove that these complex functions are important for two reasons: first, they determine the integrals of motion, and second they determine the existence of some geometric structures (in this particular case, quasi-bi-Hamiltonian structures). All the results depend on three parameters (k(1), k(2), k(3)) in such a way that in the particular case k(1) not equal 0, k(2) = k(3) = 0, the properties characterizing the Kepler problem are obtained. This paper can be considered as divided in two parts and every part presents a different approach (different complex functions and different quasi-bi-Hamiltonian structures).
000118159 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000118159 592__ $$a0.26$$b2021
000118159 590__ $$a0.737$$b2021
000118159 593__ $$aApplied Mathematics$$c2021$$dQ3
000118159 591__ $$aPHYSICS, MATHEMATICAL$$b50 / 56 = 0.893$$c2021$$dQ4$$eT3
000118159 593__ $$aMechanics of Materials$$c2021$$dQ3
000118159 591__ $$aMATHEMATICS, APPLIED$$b232 / 267 = 0.869$$c2021$$dQ4$$eT3
000118159 593__ $$aGeometry and Topology$$c2021$$dQ3
000118159 594__ $$a1.3$$b2021
000118159 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000118159 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica
000118159 773__ $$g13, 2 (2021), 195-208$$tJOURNAL OF GEOMETRIC MECHANICS$$x1941-4889
000118159 8564_ $$s341107$$uhttps://zaguan.unizar.es/record/118159/files/texto_completo.pdf$$yPostprint
000118159 8564_ $$s1223543$$uhttps://zaguan.unizar.es/record/118159/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000118159 909CO $$ooai:zaguan.unizar.es:118159$$particulos$$pdriver
000118159 951__ $$a2023-05-18-15:52:44
000118159 980__ $$aARTICLE