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Articles, 21 registres trobats
Articles 21 registres trobats  1 - 10següentfinal  anar al registre:
1.
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  
2.
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, Vol. 28, Issue 11 (December 2018) , art. 1850145  
3.
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  
4.
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  
5.
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 D. S. (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  
6.
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  
7.
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  
8.
33 p, 583.3 KB The geometry of quadratic polynomial differential systems with a finite and an infinite saddle-node (A,B) / Artés, 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)  
9.
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  
10.
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 Ricardo (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  

Articles : 21 registres trobats   1 - 10següentfinal  anar al registre:
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