Bifurcation diagrams and quotient topological spaces under the action of the affine group on a subclass of quadratic vector fields
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DIACONESCU, Oxana; SCHLOMIUK, Dana; VULPE, Nicolae. Bifurcation diagrams and quotient topological spaces under the action of the affine group on a subclass of quadratic vector fields. In: Conference of Mathematical Society of the Republic of Moldova. 3, 19-23 august 2014, Chișinău. Chișinău: "VALINEX" SRL, 2014, pp. 183-186. ISBN 978-9975-68-244-2.
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Conference of Mathematical Society of the Republic of Moldova
3, 2014
Conferința "Conference of Mathematical Society of the Republic of Moldova"
Chișinău, Moldova, 19-23 august 2014

Bifurcation diagrams and quotient topological spaces under the action of the affine group on a subclass of quadratic vector fields

Pag. 183-186

Diaconescu Oxana1, Schlomiuk Dana1, Vulpe Nicolae2
 
1 Université de Montréal,
2 Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 9 octombrie 2017


Rezumat

In this article we consider the class QSLpc qc r;1 4 of all real quadratic differential systems dx dt = p(x; y), dy dt = q(x; y) with gcd(p; q) = 1, having invariant lines of total multiplicity four and one real and two complex infinite singularities. We construct compactified canonical forms for this class and bifurcation diagrams for these compactified canonical forms. These diagrams contain many repetitions of phase portraits due to symmetries under the action of the group of affine transformations and time homotheties. We construct the orbit spaces under this action and the corresponding bifurcation diagrams in these orbit spaces. These diagrams retain only the essence of the dynamics and thus make transparent their content.

Cuvinte-cheie
quadratic differential system, Group action, phase portrait, bifurcation diagram,

topological equivalence