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Liouvillian first integrals for Liénard polynomial differential systems
Author(s):
J.
Llibre;
C.
Valls
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3229-3239.
MSC (2010):
Primary 37K10, 34D30
Posted:
April 9, 2010
MathSciNet review:
2653953
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Additional information
Abstract:
We characterize the Liouvillian first integrals for the Liénard polynomial differential systems of the form  ,  , with  and  is an arbitrary polynomial. For obtaining this result we need to find all the Darboux polynomials and the exponential factors of these systems.
References:
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Additional Information:
J.
Llibre
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
Email:
jllibre@mat.uab.cat
C.
Valls
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1049-001, Lisboa, Portugal
Email:
cvalls@math.ist.utl.pt
DOI:
10.1090/S0002-9939-10-10338-4
PII:
S 0002-9939(10)10338-4
Keywords:
Darboux polynomials,
exponential factors,
Liouvillian first integrals,
Li\'enard polynomial differential systems
Received by editor(s):
September 10, 2009
Received by editor(s) in revised form:
December 16, 2009
Posted:
April 9, 2010
Communicated by:
Yingfei Yi
Copyright of article:
Copyright
2010,
American Mathematical Society
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