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Pàgina inicial > Articles > Articles publicats > Seeking Darboux polynomials |
Data: | 2015 |
Resum: | 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. |
Ajuts: | Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Birational map ; Cofactor ; Darboux polynomial ; Non-algebraic limit cycle ; Planar polynomial differential system |
Publicat a: | Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications, Vol. 139 (2015) , p. 167-186, ISSN 0167-8019 |
Postprint 24 p, 338.1 KB |