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Seeking Darboux polynomials
Ferragut, Antoni
Gasull, Armengol

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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
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

DOI: 10.1007/s10440-014-9974-0

24 p, 338.1 KB

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