On the polynomial differential systems having polynomial first integrals
García, Belen (Universidad de Oviedo. Departamento de Matemáticas)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Suárez Pérez del Río, Jesús (Universidad de Oviedo. Departamento de Matemáticas)

Date:	2012
Abstract:	We consider the class of complex planar polynomial differential systems having a polynomial first integral. Inside this class the systems having minimal polynomial first integrals without critical remarkable values are the Hamiltonian ones. Here we mainly study the subclass of polynomial differential systems such that their minimal polynomial first integrals have a unique critical remarkable value. In particular we characterize all the Li'enard polynomial differential systems ˙x = y, ˙y = −f(x)y − g(x), with f(x) and g(x) complex polynomials in the variable x, having a minimal polynomial first integral with a unique critical remarkable value.
Grants:	Ministerio de Educación y Ciencia MTM2008-06065 Ministerio de Educación y Ciencia MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2005/SGR-550
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial differential system ; Liénard differential system ; Polynomial first integral ; Critical remarkable value
Published in:	Bulletin des Sciences Mathematiques, Vol. 136 (2012) , p. 309-316, ISSN 0007-4497

DOI: 10.1016/j.bulsci.2011.11.003

Postprint 10 p, 662.0 KB

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