Abstract
© 2014, Springer Science+Business Media Dordrecht. We introduce several techniques which allow to simplify the expression of the cofactor of Darboux polynomials of polynomial differential systems in $\mathbb {R}^{n}$. 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.
Original language | English |
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Pages (from-to) | 167-186 |
Journal | Acta Applicandae Mathematicae |
Volume | 139 |
Issue number | 1 |
DOIs | |
Publication status | Published - 29 Oct 2015 |
Keywords
- Birational map
- Cofactor
- Darboux polynomial
- Non-algebraic limit cycle
- Planar polynomial differential system