TY - JOUR
T1 - Seeking Darboux Polynomials
AU - Ferragut, Antoni
AU - Gasull, Armengol
PY - 2015/10/29
Y1 - 2015/10/29
N2 - © 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.
AB - © 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.
KW - Birational map
KW - Cofactor
KW - Darboux polynomial
KW - Non-algebraic limit cycle
KW - Planar polynomial differential system
UR - https://www.scopus.com/pages/publications/84942504909
U2 - 10.1007/s10440-014-9974-0
DO - 10.1007/s10440-014-9974-0
M3 - Article
SN - 0167-8019
VL - 139
SP - 167
EP - 186
JO - Acta Applicandae Mathematicae
JF - Acta Applicandae Mathematicae
IS - 1
ER -