caa a22 4500 606166343 CHVBK 20210128100657.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10440-014-9974-0 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9974-0 Seeking Darboux Polynomials [Elektronische Daten] [Antoni Ferragut, Armengol Gasull] 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. Springer Science+Business Media Dordrecht, 2014 Planar polynomial differential system nationallicence Darboux polynomial nationallicence Cofactor nationallicence Birational map nationallicence Non-algebraic limit cycle nationallicence Ferragut Antoni Institut de Matemàtiques i Aplicacions de Castelló (IMAC) and Departament de Matemàtiques, Universitat Jaume I, Edifici TI (ESTEC), Av. de Vicent Sos Baynat, s/n, Campus del Riu Sec, 12071, Castelló de la Plana, Spain aut Gasull Armengol Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193, Bellaterra, Barcelona, Catalonia, Spain aut Acta Applicandae Mathematicae Springer Netherlands 139/1(2015-10-01), 167-186 0167-8019 139:1<167 2015 139 10440 https://doi.org/10.1007/s10440-014-9974-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9974-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ferragut Antoni Institut de Matemàtiques i Aplicacions de Castelló (IMAC) and Departament de Matemàtiques, Universitat Jaume I, Edifici TI (ESTEC), Av. de Vicent Sos Baynat, s/n, Campus del Riu Sec, 12071, Castelló de la Plana, Spain aut NATIONALLICENCE 700 1- Gasull Armengol Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193, Bellaterra, Barcelona, Catalonia, Spain aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 139/1(2015-10-01), 167-186 0167-8019 139:1<167 2015 139 10440