The classification of a family of cubic differential systems in terms of configurations of invariant lines of the type (3, 3)
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Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (172)
Computational mathematics. Numerical analysis (102)
SM ISO690:2012
BUJAC, Cristina. The classification of a family of cubic differential systems in terms of configurations of invariant lines of the type (3, 3). In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2019, nr. 2(90), pp. 79-98. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 2(90) / 2019 / ISSN 1024-7696

The classification of a family of cubic differential systems in terms of configurations of invariant lines of the type (3, 3)

CZU: 517.977+517.98+519.6
MSC 2010: 58K45, 34C05, 34A34.

Pag. 79-98

Bujac Cristina
 
Vladimir Andrunachievici Institute of Mathematics and Computer Science
 
Disponibil în IBN: 3 ianuarie 2020


Rezumat

In this article we consider the class of non-degenerate real planar cubic vector fields, which possess two real and two complex distinct infinite singularities and invariant straight lines, including the line at infinity, of total multiplicity 7. In addition, the systems from this class possess configurations of the type (3, 3). We prove that there are exactly 16 distinct configurations of invariant straight lines for this class and present corresponding examples for the realization of each one of the detected configurations.

Cuvinte-cheie
Cubic differential system, invariant straight line, multiplicity of invariant lines, infinite and finite singularities, affine invariant polynomial, Group action, configuration of invariant lines, multiplicity of singularity