TY - JOUR
T1 - Planar real polynomial differential systems of degree n > 3 having a weak focus of high order
AU - Llibre, Jaume
AU - Rabanal, Roland
PY - 2012
Y1 - 2012
N2 - We construct planar polynomial differential systems of even (respectively odd) degree n > 3, of linear form plus a nonlinear homogeneous part of degree n having a weak focus of order n2 - 1, respectively (n2 - 1)/2, at the origin. As far as we know this provides the highest order known until now for a weak focus of a polynomial differential system of arbitrary degree n.
AB - We construct planar polynomial differential systems of even (respectively odd) degree n > 3, of linear form plus a nonlinear homogeneous part of degree n having a weak focus of order n2 - 1, respectively (n2 - 1)/2, at the origin. As far as we know this provides the highest order known until now for a weak focus of a polynomial differential system of arbitrary degree n.
KW - Center
KW - Polynomial vector fields
KW - Weak focus
UR - http://www.scopus.com/inward/record.url?scp=84873366002&partnerID=8YFLogxK
U2 - 10.1216/RMJ-2012-42-2-657
DO - 10.1216/RMJ-2012-42-2-657
M3 - Article
AN - SCOPUS:84873366002
SN - 0035-7596
VL - 42
SP - 657
EP - 693
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
IS - 2
ER -