TY - JOUR
T1 - Global phase portraits of some reversible cubic centers with collinear or infinitely many singularities
AU - Caubergh, M.
AU - Llibre, J.
AU - Torregrosa, J.
N1 - Funding Information:
The authors are partially supported by the MICIIN/FEDER grant number MTM2008-03437 and by the AGAUR grant number 2009SGR 410. Furthermore the first author is also supported by the Juan de la Cierva grant number JCI-2007-49-764 and the second author is also partially supported by ICREA Academia.
PY - 2012/11
Y1 - 2012/11
N2 - We study the reversible cubic vector fields of the form = -y + ax 2 + bxy + cy2 - y(x2 + y2), = x + dx2 + exy + fy2 + x(x2 + y2), having simultaneously a center at infinity and at the origin. In this paper, the subclass of these reversible systems having collinear or infinitely many singularities are classified with respect to topological equivalence.
AB - We study the reversible cubic vector fields of the form = -y + ax 2 + bxy + cy2 - y(x2 + y2), = x + dx2 + exy + fy2 + x(x2 + y2), having simultaneously a center at infinity and at the origin. In this paper, the subclass of these reversible systems having collinear or infinitely many singularities are classified with respect to topological equivalence.
KW - Center-focus problem
KW - cubic vector fields
KW - global classification of phase portraits
KW - reversible planar vector fields
UR - http://www.scopus.com/inward/record.url?scp=84871002634&partnerID=8YFLogxK
U2 - 10.1142/S0218127412502732
DO - 10.1142/S0218127412502732
M3 - Article
AN - SCOPUS:84871002634
SN - 0218-1274
VL - 22
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
IS - 11
M1 - 1250273
ER -