Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C2.

Colin Christopher; Christiane Rousseau

Publicacions Matemàtiques (2001)

  • Volume: 45, Issue: 1, page 95-123
  • ISSN: 0214-1493

Abstract

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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.

How to cite

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Christopher, Colin, and Rousseau, Christiane. "Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C2.." Publicacions Matemàtiques 45.1 (2001): 95-123. <http://eudml.org/doc/41416>.

@article{Christopher2001,
abstract = {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.},
author = {Christopher, Colin, Rousseau, Christiane},
journal = {Publicacions Matemàtiques},
keywords = {Sistemas complejos; Cuádricas complejas; Sistemas diferenciales; Curvas algebraicas planas; linearizability; complex quadratic systems; complex cubic systems; real saddles; bifurcation diagrams},
language = {eng},
number = {1},
pages = {95-123},
title = {Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C2.},
url = {http://eudml.org/doc/41416},
volume = {45},
year = {2001},
}

TY - JOUR
AU - Christopher, Colin
AU - Rousseau, Christiane
TI - Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C2.
JO - Publicacions Matemàtiques
PY - 2001
VL - 45
IS - 1
SP - 95
EP - 123
AB - 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.
LA - eng
KW - Sistemas complejos; Cuádricas complejas; Sistemas diferenciales; Curvas algebraicas planas; linearizability; complex quadratic systems; complex cubic systems; real saddles; bifurcation diagrams
UR - http://eudml.org/doc/41416
ER -

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