Liouvillian integrability versus Darboux polynomials
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)

Date:	2016
Abstract:	In this note we provide a sufficient condition on the existence of Darboux polynomials of polynomial differential systems via existence of Jacobian multiplier or of Liouvillian first integral and a degree condition among different components of the system. As an application of our main results we prove that the Liénard polynomial differential system x ̇ = y, y ̇ = − f (x)y − g(x) with deg f > deg g is not Liouvillian integrable.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 318999 European Commission 316338
Note:	Agraïments: FEDER/UNAB10-4E-378. The second author is supported by Portuguese National Funds through FCT - Fundacâo para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD. The third author is partially supported by NNSF of China grant number 11271252, by RFDP of Higher Education of China grant number 20110073110054, and by FP7-PEOPLE-2012-IRSES-316338 of Europe.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Darboux Jacobian multiplier ; Darboux polynomial ; Liouvillian integrability ; Polynomial differential systems
Published in:	Qualitative theory of dynamical systems, Vol. 15 (2016) , p. 503-515, ISSN 1662-3592

DOI: 10.1007/s12346-016-0212-1

Postprint 13 p, 810.8 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles