Results overview: Found 8 records in 0.02 seconds.
Articles, 8 records found
Articles 8 records found  
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.
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  
3.
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  
4.
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  
5.
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  
6.
40 p, 1.5 MB Geometric configurations of singularities for quadratic differential systems with total finite multiplicity lower than 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 [3] we classified globally the configurations of singularities at infinity of quadratic differential systems, with respect to the geometric equivalence relation. The global classification of configurations of finite singularities was done in [2] modulo the coarser topological equivalence relation for which no distinctions are made between a focus and a node and neither are they made between a strong and a weak focus or between foci of different orders. [...]
2013
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica., Vol. 71 Núm. 1 (2013) , p. 72-124  
7.
53 p, 2.7 MB From topological to geometric equivalence in the classification of singularities at infinity for quadratic vector fields / 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 the topological classification of phase portraits no distinctions are made between a focus and a node and neither are they made between a strong and a weak focus or between foci of different orders. [...]
2015 - 10.1216/RMJ-2015-45-1-29
The Rocky Mountain Journal of Mathematics, Vol. 45 Núm. 1 (2015) , p. 29-113  
8.
60 p, 2.7 MB Global configurations of singularities for quadratic differential systems with exactly three 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) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques) ; Vulpe, Nicolae (Academy of Science of Moldova)
In this article we obtain the geometric classification of singularities, finite and infinite, for the two subclasses of quadratic differential systems with total finite multiplicity m_f=4 possessing exactly three finite singularities, namely: systems with one double real and two complex simple singularities (31 configurations) and (ii) systems with one double real and two simple real singularities (265 configurations). [...]
2015 - 10.14232/ejqtde.2015.1.49
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 49 (2015) , p. 1-60  

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