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Articles 24 registres trobats  anterior11 - 20següent  anar al registre: La cerca s'ha fet en 0.02 segons. 
11.
33 p, 583.3 KB The geometry of quadratic polynomial differential systems with a finite and an infinite saddle-node (A,B) / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Rezende, Alex C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
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. [...]
2014 - 10.1142/S0218127414500448
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 24 Núm. 4 (2014) , p. 1450044 (30 pages)  
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12.
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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13.
12 p, 370.0 KB Piecewise bounded quadratic systems in the plane / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; da Silva, Clayton Eduardo Lente (UNESP(Brazil). Deparatamento de Matemática) ; Da Silva, Paulo R. (UNESP(Brazil). Deparatamento de Matemática)
In this paper we study the sliding mode of piecewise bounded quadratic systems in the plane given by a non-smooth vector field Z = (X, Y ). Analyzing the singular, crossing and sliding sets, we get the conditions which ensure that any solution, including the sliding one, is bounded.
2014 - 10.1007/s12591-014-0205-y
Differential Equations and Dynamical Systems, 2014  
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14.
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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15.
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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16.
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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17.
28 p, 571.0 KB Complete geometric invariant study of two classes of quadratic systems / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
In this paper we give a complete study using affine invariant conditions for the quadratic systems having centers. Independently we do the same for quadratic systems being Hamiltonian. There are two improvements of the previous results as [29] in which centers where study up to GL-invariant, and of [1] in which Hamiltonian QS where classified without invariants. [...]
2012
Electronic journal of differential equations, Vol. 2012 Núm. 9 (2012) , p. 1-35  
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18.
38 p, 831.0 KB Quadratic systems with an integrable saddle: A complete classification in the coefficient space R^12 / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
A quadratic polynomial differential system can be identified with a single point of R12 through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of R12 having an integrable saddle. [...]
2012 - 10.1016/j.na.2012.04.043
Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 5416-5447  
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19.
16 p, 625.7 KB Liouvillian first integrals of quadratic-linear polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Instituto Superior Técnico (Lisboa). Departamento de Matemática)
For a large class of quadratic-linear polynomial differential systems with a unique singular point at the origin having non-zero eigenvalues, we classify the ones which have a Liouvillian first integral, and we provide the explicit expression of them.
2011 - 10.1016/j.jmaa.2010.12.033
Journal of mathematical analysis and applications, Vol. 379 (2011) , p. 188-199  
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20.
20 p, 347.7 KB Planar vector fields with a given set of orbits / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
We determine all the C 1 planar vector fields with a given set of orbits of the form y − y(x) = 0 satisfying convenient assumptions. The case when these orbits are branches of an algebraic curve is also study. [...]
2011 - 10.1007/s10884-011-9219-0
Journal of dynamics and differential equations, Vol. 23 Núm. 4 (2011) , p. 885-902  
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