Seeking Darboux polynomials
Ferragut Amengual, Antoni Manel (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2015
Abstract:	We introduce several techniques which allow to simplify the expression of the cofactor of Darboux polynomials of polynomial differential systems in R^n. We apply these techniques to some well-known systems when n = 2, 3, 4. We also propose a general method for computing Darboux polynomials in the plane. As an application we prove that a family of potential systems, that includes the van der Pol one, has no Darboux polynomials, giving in particular a new simple proof that the van der Pol limit cycle is not algebraic.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Birational map ; Cofactor ; Darboux polynomial ; Non-algebraic limit cycle ; Planar polynomial differential system
Published in:	Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications, Vol. 139 (2015) , p. 167-186, ISSN 0167-8019

DOI: 10.1007/s10440-014-9974-0

Postprint 24 p, 338.1 KB

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