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Artículos Encontrados 24 registros  1 - 10siguientefinal  ir al registro: La búsqueda tardó 0.01 segundos. 
1.
18 p, 772.0 KB Phase Portraits of Families VII and VIII of the Quadratic Systems / Cairó, Laurent (Université d'Orleans. Institut Denis Poisson) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The quadratic polynomial differential systems in a plane are the easiest nonlinear differential systems. They have been studied intensively due to their nonlinearity and the large number of applications. [...]
2023 - 10.3390/axioms12080756
Axioms, Vol. 12, Issue 8 (August 2023) , art. 756  
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2.
52 p, 1.1 MB Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e Computação) ; Rodrigues, Camila A. B. (Universidade Federal de Santa Catarina. Departamento de Matemática (Brazil))
Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its subclass formed by the systems possessing an invariant cubic f(x, y) = 0. In this article, using the action of the group of real affine transformations and time rescaling on QS, we obtain all the possible normalforms for the quadratic systems in QS3. [...]
2021
Electronic journal of differential equations, Vol. 2021, Issue 69 (2021) , p. 1-52
2 documentos
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3.
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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4.
22 p, 510.1 KB Quadratic systems with a rational first integral of degree three : A complete classification in the coefficient space ℝ12 / 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 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  
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5.
11 p, 796.2 KB Algebraic limit cycles bifurcating from algebraic ovals of quadratic centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tian, Yun (Shanghai Normal University. Department of Mathematics)
In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles. [...]
2018 - 10.1142/S0218127418501456
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, Issue 11 (December 2018) , art. 1850145  
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6.
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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7.
17 p, 570.2 KB Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Messias, Marcelo (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil)) ; Reinol, Alisson C. (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil))
In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C and C as invariant algebraic curves and the function H=C C , with α and β real values, as first integral. [...]
2017 - 10.1080/14689367.2016.1263600
Dynamical Systems, Vol. 32, Issue 3 (2017) , p. 374-390  
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8.
15 p, 365.0 KB Quadratic systems with an invariant conic having Darboux invariants / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de Sâo Paulo (Brazil). Departamento de Matemática)
The complete characterization of the phase portraits of real planar quadratic vector fields is very far to be completed. As this attempt is not possible in the whole class due to the large number of parameters (twelve, but, after affine transformations and time rescaling, we arrive at families with five parameters, which is still a big number of parameters), many subclasses have been considered and studied. [...]
2018 - 10.1142/S021919971750033X
Communications in contemporaray mathematics, Vol. 20, issue 4 (2018) , art. 1750033  
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9.
43 p, 1.7 MB Geometric configurations of singularities for quadratic differential systems with three distinct real simple finite 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 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  
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10.
15 p, 739.0 KB Liouvillian and analytic integrability of the quadratic vector fields having an invariant ellipse / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant ellipse. More precisely, a quadratic system having an invariant ellipse can be written into the form ˙x = x2+y2−1+y(ax+by+c), ˙y = −x(ax+by+c), and the ellipse becomes x2+y2 = 1. [...]
2014 - 10.1007/s10114-014-2484-1
Acta Mathematica Sinica. English Series, Vol. 30 Núm. 3 (2014) , p. 453-466  
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Artículos : Encontrados 24 registros   1 - 10siguientefinal  ir al registro:
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