In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. The sufficiency of these conditions is shown by exhibiting explicitly a linearizing change of coordinates, either of Darboux type or a generalization of it.
@article{urn:eudml:doc:41416,
title = {Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C2.},
journal = {Publicacions Matem\`atiques},
volume = {45},
year = {2001},
pages = {95-123},
mrnumber = {MR1829579},
zbl = {0984.34023},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41416}
}
Christopher, Colin; Rousseau, Christiane. Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C2.. Publicacions Matemàtiques, Tome 45 (2001) pp. 95-123. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41416/