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Results overview: Found 12 records in 0.05 seconds.
Articles, 11 records found
Research literature, 1 records found
Articles 11 records found  1 - 10next  jump to record:
1.
25 p, 548.4 KB Invariant conditions for phase portraits of quadratic systems with complex conjugate invariant lines meeting at a finite point / Artés Ferragud, 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, vol. 70 (July 2020) p. 923-945  
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2.
129 p, 4.9 MB Geometric and algebraic classification of quadratic differential systems with invariant hyperbolas / Oliveira, Regilene (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
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3.
53 p, 809.9 KB Family of quadratic differential systems with invariant hyperbolas: a complete classification in the space R12 / Oliveira, Regilene (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
Detailed record - Creative Commons
4.
27 p, 2.2 MB Global topological configurations of singularities for the whole family of quadratic differential systems / Artés Ferragud, 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 Sciences 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  
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5.
62 p, 2.4 MB Geometric configurations of singularities for quadratic differential systems with total finite multiplicity m_f=2 / Artés Ferragud, 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 Sciences 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  
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6.
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 Ferragud, 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 Sciences 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  
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7.
36 p, 1.5 MB Global configurations of singularities for quadratic differential systems with exactly two finite singularities of total multiplicity four / Artés Ferragud, 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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8.
40 p, 1.5 MB Geometric configurations of singularities for quadratic differential systems with total finite multiplicity lower than 2 / Artés Ferragud, 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 Sciences 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  
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9.
53 p, 2.7 MB From topological to geometric equivalence in the classification of singularities at infinity for quadratic vector fields / Artés Ferragud, 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 Sciences 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  
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10.
60 p, 2.7 MB Global configurations of singularities for quadratic differential systems with exactly three finite singularities of total multiplicity four / Artés Ferragud, 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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Articles : 11 records found   1 - 10next  jump to record:
Research literature 1 records found  
1.
372 p, 4.1 MB The geometry of some tridimensional families of planar quadratic differential systems / Rezende, Alex C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Artés Ferragud, Joan Carles, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene Delazari dos Santos, dir.
Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. [...]
[São Paolo] Universidade de São Paolo 2014  
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