Institutul de Matematică şi Informatică "Vladimir Andrunachievici"

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The Family of Quadratic Systems with Two Invariant Conics: Parabola and Hyperbola [Articol]
(2024) Vulpe, Nicolae
We consider the family of quadratic systems QSPHη>0 having three real distinct infinite singularities and possessing at least two invariant conics: a parabola and a hyperbola. All the possible configurations of these invariant conics including invariant lines (when they exist) are determined. We describe completely the set of such systems and we prove the existence of exactly 38 distinct configurations which could possess a system in this family.
Polynomial Differential Cubic Systems with Invariant Straight Lines of Total Multiplicity Seven and Four Distinct Infinite Singularities [Articol]
(2024) Bujac, Cristina; Vulpe, Nicolae
The family of cubic differential systems possessing invariant straight lines was considered by many authors. But a strong classification of this family according to the configurations of invariant lines began in 2006 [11], where the existence of the maximum number of invariant lines (nine) is required. Here we continue the investigation of the subfamily of cubic systems possessing invariant lines of total multiplicity seven and four distinct infinite singularities. We prove that this subfamily could have a total of 166 distinct configurations of invariant straight lines.