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Liouvillian integrability versus Darboux polynomials
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia (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.
Note: Número d'acord de subvenció MINECO/MTM2008-03437
Note: Número d'acord de subvenció AGAUR/2009/SGR-410
Note: Número d'acord de subvenció EC/FP7/2012/318999
Note: Número d'acord de subvenció EC/FP7/2012/316338
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 ; submittedVersion
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


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

 Record created 2017-01-23, last modified 2019-02-02



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