000058513 001__ 58513 000058513 005__ 20170504101037.0 000058513 0247_ $$2doi$$a10.3842/SIGMA.2013.026 000058513 0248_ $$2sideral$$a81275 000058513 037__ $$aART-2013-81275 000058513 041__ $$aeng 000058513 100__ $$0(orcid)0000-0003-4480-6535$$aCariñena , J.F.$$uUniversidad de Zaragoza 000058513 245__ $$aA quasi-Lie schemes approach to second-order Gambier equations 000058513 260__ $$c2013 000058513 5060_ $$aAccess copy available to the general public$$fUnrestricted 000058513 5203_ $$aA quasi-Lie scheme is a geometric structure that provides t-dependent changes of variables transforming members of an associated family of systems of first-order differential equations into members of the same family. In this note we introduce two quasi-Lie schemes for studying second-order Gambier equations in a geometric way. This allows us to study the transformation of these equations into simpler canonical forms, which solves a gap in the previous literature, and other relevant differential equations, which leads to derive new constants of motion for families of second-order Gambier equations. Additionally, we describe general solutions of certain second-order Gambier equations in terms of particular solutions of Riccati equations, linear systems, and t-dependent frequency harmonic oscillators. 000058513 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-1$$9info:eu-repo/grantAgreement/ES/DGA/FMI40-10$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2009-11154 000058513 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-sa$$uhttp://creativecommons.org/licenses/by-nc-sa/3.0/es/ 000058513 590__ $$a1.299$$b2013 000058513 591__ $$aPHYSICS, MATHEMATICAL$$b25 / 55 = 0.455$$c2013$$dQ2$$eT2 000058513 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000058513 700__ $$aGuha , P. 000058513 700__ $$aDe Lucas, J. 000058513 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDepartamento de Física Teórica$$cFísica Teórica 000058513 773__ $$g9, 26 (2013), [23 pp]$$pSymmetry Integrability and Geometry-Methods and Applications$$tSymmetry Integrability and Geometry-Methods and Applications$$x1815-0659 000058513 8564_ $$s418994$$uhttps://zaguan.unizar.es/record/58513/files/texto_completo.pdf$$yVersión publicada 000058513 8564_ $$s92115$$uhttps://zaguan.unizar.es/record/58513/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000058513 909CO $$ooai:zaguan.unizar.es:58513$$particulos$$pdriver 000058513 951__ $$a2017-05-04-10:07:58 000058513 980__ $$aARTICLE