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Articles 16 records found  1 - 10next  jump to record:
1.
Invariant conditions for phase portraits of quadratic systems with complex conjugate invariant lines meeting at a finite point / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques (France)) ; Vulpe, Nicolae (Vladimir Andrunakievichi Institute of Mathematics and Computer Science (Moldova))
The goal of this article is to give invariant necessary and sufficient conditions for a quadratic system, presented in whatever normal form, to have anyone of 17 out of the 20 phase portraits of the family of quadratic systems with two complex conjugate invariant lines intersecting at a finite real point. [...]
2020 - 10.1007/s12215-020-00541-2
Rendiconti del Circolo Matematico di Palermo, (July 2020)  
2.
22 p, 510.1 KB Quadratic systems with a rational first integral of degree three : A complete classification in the coefficient space ℝ12 / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science (Moldova))
A quadratic polynomial differential system can be identified with a single point of ℝ12 through its coefficients. The phase portrait of the quadratic systems having a rational first integral of degree 3 have been studied using normal forms. [...]
2010 - 10.1007/s12215-010-0032-0
Rendiconti del Circolo Matematico di Palermo, Vol. 59, Issue 3 (December 2010) , p. 419-449  
3.
129 p, 4.9 MB Geometric and algebraic classification of quadratic differential systems with invariant hyperbolas / Oliveira, Regilene D. S. (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação) ; Rezende, Alex C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
Let QSH be the whole class of non-degenerate planar quadratic differential systems possessing at least one invariant hyperbola. We classify this family of systems, modulo the action of the group of real affine transformations and time rescaling, according to their geometric properties encoded in the configurations of invariant hyperbolas and invariant straight lines which these systems possess. [...]
2017
Electronic journal of differential equations, Vol. 2017, Issue 295 (2017) , p. 1-122
2 documents
4.
53 p, 809.9 KB Family of quadratic differential systems with invariant hyperbolas: a complete classification in the space R12 / Oliveira, Regilene D. S. (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação) ; Rezende, Alex C. (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
In this article we consider the class QS of all non-degenerate quadratic systems. A quadratic polynomial differential system can be identified with a single point of R12 through its coefficients. In this paper using the algebraic invariant theory we provided necessary and sufficient conditions for a system in QS to have at least one invariant hyperbola in terms of its coefficients. [...]
2016
Electronic journal of differential equations, Vol. 2016, Issue 162 (2016) , p. 1-50
2 documents
5.
Global topological configurations of singularities for the whole family of quadratic differential systems / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science)
In Artés et al. (Geometric configurations of singularities of planar polynomial differential systems. A global classification in the quadratic case. Birkhäuser, Basel, 2019) the authors proved that there are 1765 different global geometrical configurations of singularities of quadratic differential systems in the plane. [...]
2020 - 10.1007/s12346-020-00372-7
Qualitative Theory of Dynamical Systems, Vol. 19, Issue 1 (April 2020) , art. 51  
6.
22 p, 1.1 MB First integrals and phase portraits of planar polynomial differential cubic systems with the maximum number of invariant straight lines / Bujac, Cristina (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science)
In the article LliVul2006 the family of cubic polynomial differential systems possessing invariant straight lines of total multiplicity 9 was considered and 23 such classes of systems were detected. We recall that 9 invariant straight lines taking into account their multiplicities is the maximum number of straight lines that a cubic polynomial differential systems can have if this number is finite. [...]
2016 - 10.1007/s12346-016-0211-2
Qualitative theory of dynamical systems, Vol. 15 (2016) , p. 327-348  
7.
43 p, 1.7 MB Geometric configurations of singularities for quadratic differential systems with three distinct real simple finite singularities / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science)
In this work we classify, with respect to the geometric equivalence relation, the global configurations of singularities, finite and infinite, of quadratic differential systems possessing exactly three distinct finite simple singularities. [...]
2013 - 10.1007/s11784-014-0175-2
Journal of fixed point theory and applications, Vol. 14 Núm. 2 (2013) , p. 555-618  
8.
62 p, 2.4 MB Geometric configurations of singularities for quadratic differential systems with total finite multiplicity m_f=2 / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science)
In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [3]. [...]
2014
Electronic journal of differential equations, Vol. 2014 Núm. 159 (2014) , p. 1-79  
9.
35 p, 1.6 MB Global configurations of singularities for quadratic differential systems with total finite multiplicity three and at most two real singularities / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Science of Moldova. Institute of Mathematics and Computer Science)
In this work we consider the problem of classifying all configurations of singularities, finite and infinite, of quadratic differential systems, with respect to the geometric equivalence relation defined in [2]. [...]
2014 - 10.1007/s12346-014-0119-7
Qualitative Theory of Dynamical Systems, Vol. 13 (2014) , p. 305-351  
10.
36 p, 1.5 MB Global configurations of singularities for quadratic differential systems with exactly two finite singularities of total multiplicity four / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Rezende, Alex C. (Universidade de São Paulo) ; Schlomiuk, Dana (Université de Montréal) ; Vulpe, Nicolae (Academy of Science of Moldova)
In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [2]. [...]
2014 - 10.14232/ejqtde.2014.1.60
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 60 (2014) , p. 1-43  

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1 Vulpe, N. I.
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