000077272 001__ 77272 000077272 005__ 20210121114446.0 000077272 0247_ $$2doi$$a10.1063/1.4922509 000077272 0248_ $$2sideral$$a91214 000077272 037__ $$aART-2015-91214 000077272 041__ $$aeng 000077272 100__ $$0(orcid)0000-0003-4480-6535$$aCariñena, J. F.$$uUniversidad de Zaragoza 000077272 245__ $$aJacobi multipliers, non-local symmetries, and nonlinear oscillators 000077272 260__ $$c2015 000077272 5060_ $$aAccess copy available to the general public$$fUnrestricted 000077272 5203_ $$aConstants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local symmetries for such two nonlinear oscillators is proved. 000077272 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-1$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2011-15725-E$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2012-33575 000077272 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000077272 590__ $$a1.234$$b2015 000077272 591__ $$aPHYSICS, MATHEMATICAL$$b25 / 53 = 0.472$$c2015$$dQ2$$eT2 000077272 592__ $$a0.792$$b2015 000077272 593__ $$aStatistical and Nonlinear Physics$$c2015$$dQ2 000077272 593__ $$aMathematical Physics$$c2015$$dQ2 000077272 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000077272 700__ $$aDe Lucas, J. 000077272 700__ $$0(orcid)0000-0002-8402-2332$$aRañada, M. F.$$uUniversidad de Zaragoza 000077272 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000077272 773__ $$g56, 6 (2015), 063505$$pJ. math. phys.$$tJOURNAL OF MATHEMATICAL PHYSICS$$x0022-2488 000077272 8564_ $$s276773$$uhttps://zaguan.unizar.es/record/77272/files/texto_completo.pdf$$yPostprint 000077272 8564_ $$s96097$$uhttps://zaguan.unizar.es/record/77272/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000077272 909CO $$ooai:zaguan.unizar.es:77272$$particulos$$pdriver 000077272 951__ $$a2021-01-21-10:43:20 000077272 980__ $$aARTICLE