The generalized Liénard polynomial differential systems x'=y,y'= -g(x) - f (x)y with deg g = deg f 1 are not Liouvillian integrable
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Instituto Superior Técnico. Departamento de Matemática)

Date:	2015
Abstract:	We prove the nonexistence of Liouvillian first integrals for the generalized Li\'enard polynomial differential systems of the form x' = y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that g = f 1.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410 European Commission 316338 European Commission 318999
Note:	Agraïments: The second author was supported by Portuguese National Funds through FCT - Fundação para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD (PEst-OE/EEI/LA0009/2013)
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Darboux polynomial ; Exponential factor ; Liénard polynomial differential system ; Liouvillian first integrals
Published in:	Bulletin des Sciences Mathematiques, Vol. 139 (2015) , p. 214-227, ISSN 0007-4497

DOI: 10.1016/j.bulsci.2014.08.010

Postprint 10 p, 720.5 KB

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