UAB Digital Repository of Documents 18 records found  1 - 10next  jump to record: Search took 0.03 seconds. 
1.
14 p, 238.1 KB Limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Lopes, Bruno D. (Universidade Estadual de Campinas (Brasil). Instituto de Matemática, Estatística e Computação Científica) ; De Moraes, Jaime R. (Universidad Estatal de Mato Grosso del Sur (Brasil))
In this paper we obtain two explicit polynomials, whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of polynomial differential centers of order 5, when this family is perturbed inside the class of all polynomial differential systems of order 5, whose average function of first order is not zero. [...]
2018
Electronic journal of differential equations, Vol. 2018, No. 118 (2018) , p. 1-14  
2.
7 p, 170.1 KB Normal forms and hyperbolic algebraic limit cycles for a class of polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàticaa)
We study the normal forms of polynomial systems having a set of invariant algebraic curves with singular points. We provide sufficient conditions for the existence of hyperbolic algebraic limit cycles.
2018
Electronic journal of differential equations, Vol. 2018, no. 83 (2018) , p. 1-7  
3.
24 p, 759.4 KB Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yu, Jiang (Shanghai Jiao Tong University. Department of Mathematics)
In this article we consider a class of quadratic polynomial differential systems in the plane having a hyperbola and a straight line as invariant algebraic curves, and we classify all its phase portraits. [...]
2018
Electronic journal of differential equations, Vol. 141 (2018) , p. 1-19  
4.
13 p, 299.6 KB On a Class of Invariant Algebraic Curves for Kukles Systems / Osuna, Osvaldo (UMSNH(México). Instituto de Física y Matemáticas) ; Rebollo-Perdomo, Salomón (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villaseñor, Gabriel (Instituto Tecnológico de Morelia(México). Departamento de Ciencias Básicas)
In this paper we give a new upper bound for the degree of a class of transversal to infinity invariant algebraic curves for polynomial Kukles systems of arbitrary degree. Moreover, we prove that a quadratic Kukles system having at least one transversal to infinity invariant algebraic curve is integrable.
2016 - 10.14232/ejqtde.2016.1.61
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2016 Núm. 61 (2016) , p. 1-12  
5.
12 p, 363.9 KB Analytic reducibility of nondegenerate centers: Cherkas systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems x˙ = y, y˙ = P0(x) + P1(x)y + P2(x)y2, where Pi(x) are polynomials of degree n, P0(0) = 0 and P′0(0) < 0. [...]
2016 - 10.14232/ejqtde.2016.1.49
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 49 (2016) , p. 1-10  
6.
23 p, 384.6 KB Centers of projective vector fields of spatial quasi-homogeneous systems with weight (m,m,n) and degree 2 on the sphere / Liang, Haihua (Guangdong Polytechnic Normal University(China). Department of Computer Science) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the centers of projective vector fields Q_T of three-dimensional quasi-homogeneous differential system d/dt=Q() with the weight (m,m,n) and degree 2 on the unit sphere S^2. We seek the sufficient and necessary conditions under which Q_T has at least one center on S^2. [...]
2016 - 10.14232/ejqtde.2016.1.103
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 103 (2016) , p. 1-26  
7.
17 p, 401.0 KB Global phase portraits of quadratic systems with an ellipse and a straight line as invariant algebraic curves / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yu, Jiang (Shanghai Jiao Tong University. Department of Mathematics)
In this article we study a class of integrable quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having an ellipse and a straight line as invariant algebraic curves. [...]
2015
Electronic Journal of Differential Equations, Vol. 314 (2015) , p. 1-14  
8.
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  
9.
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  
10.
9 p, 763.1 KB Limit cycles for a class of discontinuous generalized Liénard polynomial differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (UFSCar(Brazil). Department of Physics, Chemistry and Mathematics)
We divide R2 in l sectors S1, . . . , Sl, with l > 1 even. We define in R2 a discontinuous differential system such that in each sector Sk, for k = 1, . . . , l, is defined a smooth generalized Lienard polynomial differential equation ¨x + fi(x) ˙x + gi(x) = 0, i = 1, 2 alternatively, where fi and gi are polynomials of degree n−1 and m respectively. [...]
2013
Electronic Journal of Differential Equations, Vol. 2013 Núm. 195 (2013) , p. 1-8  

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