Classification of quadratic systems possessing an invariant conic and a Darboux invariant
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VULPE, Nicolae; SCHLOMIUK, Dana. Classification of quadratic systems possessing an invariant conic and a Darboux invariant. In: Conference of Mathematical Society of the Republic of Moldova. 4, 28 iunie - 2 iulie 2017, Chişinău. Chişinău: Centrul Editorial-Poligrafic al USM, 2017, pp. 347-350. ISBN 978-9975-71-915-5.
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Conference of Mathematical Society of the Republic of Moldova
4, 2017
Conferința "Conference of Mathematical Society of the Republic of Moldova"
Chişinău, Moldova, 28 iunie - 2 iulie 2017

Classification of quadratic systems possessing an invariant conic and a Darboux invariant

Pag. 347-350

Vulpe Nicolae1, Schlomiuk Dana2
 
1 Institute of Mathematics and Computer Science ASM,
2 Université de Montréal
 
Disponibil în IBN: 5 octombrie 2017


Rezumat

In this article we consider the family of quadratic differential systems having an invariant conic C : f(x, y) = 0, and a Darboux invariant of the form f(x, y)est with s ∈ R \ {0} (where t is the time). Applying the algebraic theory of invariants of differential equations we present a complete classification of this family of quadratic systems. First we detect necessary and sufficient conditions for an arbitrary quadratic system to be in this class. Secondly, we construct affine invariant criteria for the realization of each one of the possible phase portraits of the systems in this family.

Cuvinte-cheie
quadratic differential system, invariant conic, phase portrait, Group action, affine invariant polynomial,

Darboux invariant