000077153 001__ 77153 000077153 005__ 20190218160629.0 000077153 0247_ $$2doi$$a10.4064/bc110-0-2 000077153 0248_ $$2sideral$$a108674 000077153 037__ $$aART-2016-108674 000077153 041__ $$aeng 000077153 100__ $$0(orcid)0000-0003-4480-6535$$aCariñena, J.F.$$uUniversidad de Zaragoza 000077153 245__ $$aGeneralized Lie approach to integrability by quadratures 000077153 260__ $$c2016 000077153 5060_ $$aAccess copy available to the general public$$fUnrestricted 000077153 5203_ $$aAfter a short review of the classical Lie theorem, a finite-dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way are discussed, determining also the number of quadratures needed to integrate the system. The theory is illustrated with examples, and an extension of the theorem where the Lie algebras are replaced by some distributions is also presented. 000077153 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-1$$9info:eu-repo/grantAgreement/ES/DGA/E24-2$$9info:eu-repo/grantAgreement/ES/MINECO/FPA2015-65745-P$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2015-64166-C2-1-P 000077153 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000077153 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000077153 700__ $$0(orcid)0000-0002-0882-0463$$aFalceto, F.$$uUniversidad de Zaragoza 000077153 700__ $$aGrabowski, J. 000077153 700__ $$0(orcid)0000-0002-8402-2332$$aRañada, M. F.$$uUniversidad de Zaragoza 000077153 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000077153 773__ $$g110 (2016), 25-40$$pBanach Cent. Publ.$$tBanach Center Publications$$x0137-6934 000077153 8564_ $$s380474$$uhttps://zaguan.unizar.es/record/77153/files/texto_completo.pdf$$yVersión publicada 000077153 8564_ $$s52364$$uhttps://zaguan.unizar.es/record/77153/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000077153 909CO $$ooai:zaguan.unizar.es:77153$$particulos$$pdriver 000077153 951__ $$a2019-02-18-13:36:00 000077153 980__ $$aARTICLE