000048098 001__ 48098 000048098 005__ 20200221144246.0 000048098 0247_ $$2doi$$a10.3842/SIGMA.2016.010 000048098 0248_ $$2sideral$$a93634 000048098 037__ $$aART-2016-93634 000048098 041__ $$aeng 000048098 100__ $$0(orcid)0000-0003-4480-6535$$aCariñena, J. F.$$uUniversidad de Zaragoza 000048098 245__ $$aQuasi-Bi-Hamiltonian structures of the 2-dimensional Kepler problem 000048098 260__ $$c2016 000048098 5060_ $$aAccess copy available to the general public$$fUnrestricted 000048098 5203_ $$aThe existence of quasi-bi-Hamiltonian structures for the Kepler problem is studied. We first relate the superintegrability of the system with the existence of two complex functions endowed with very interesting Poisson bracket properties and then we prove the existence of a quasi-bi-Hamiltonian structure by making use of these two functions. The paper can be considered as divided in two parts. In the first part a quasi-bi-Hamiltonian structure is obtained by making use of polar coordinates and in the second part a new quasi-bi-Hamiltonian structure is obtained by making use of the separability of the system in parabolic coordinates. 000048098 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-1$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2012-33575 000048098 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-sa$$uhttp://creativecommons.org/licenses/by-nc-sa/3.0/es/ 000048098 590__ $$a0.765$$b2016 000048098 591__ $$aPHYSICS, MATHEMATICAL$$b45 / 55 = 0.818$$c2016$$dQ4$$eT3 000048098 592__ $$a0.56$$b2016 000048098 593__ $$aAnalysis$$c2016$$dQ3 000048098 593__ $$aMathematical Physics$$c2016$$dQ3 000048098 593__ $$aGeometry and Topology$$c2016$$dQ3 000048098 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000048098 700__ $$0(orcid)0000-0002-8402-2332$$aRañada, M. F.$$uUniversidad de Zaragoza 000048098 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000048098 773__ $$g12 (2016), [16 pp.]$$pSymmetry Integrability and Geometry-Methods and Applications$$tSymmetry Integrability and Geometry-Methods and Applications$$x1815-0659 000048098 8564_ $$s354728$$uhttps://zaguan.unizar.es/record/48098/files/texto_completo.pdf$$yVersión publicada 000048098 8564_ $$s86124$$uhttps://zaguan.unizar.es/record/48098/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000048098 909CO $$ooai:zaguan.unizar.es:48098$$particulos$$pdriver 000048098 951__ $$a2020-02-21-13:24:55 000048098 980__ $$aARTICLE