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Articles, 25 registres trobats
Articles 25 registres trobats  1 - 10següentfinal  anar al registre:
1.
13 p, 271.6 KB Periodic orbits bifurcating from a nonisolated zero-Hopf equilibrium of three-dimensional differential systems revisited / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the periodic solutions bifurcating from a nonisolated zero–Hopf equilib- rium in a polynomial differential system of degree two in R³. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero–Hopf equilibrium. [...]
2018 - 10.1142/S021812741850058X
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, no. 5 (2018) , art. 1850058  
2.
21 p, 626.8 KB Phase portraits for some symmetric cubic Riccati polynomial differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene D. S. (Universidade de São Paulo. Departamento de Matemática) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We classify the topological phase portraits in the Poincaré disc of two classes of symmetric Riccati cubic polynomial differential systems.
2018 - 10.1016/j.topol.2017.11.023
Topology and its applications, Vol. 234 (fEB. 2018) , p. 220-237  
3.
25 p, 473.1 KB Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities / Huang, Jianfeng (Jinan University. Department of Mathematics) ; Liang, Haihua (Guangdong Polytechnic Normal University. School of Mathematics and Systems Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the limit cycles of the planar polynomial differential systems * x=ax-y P_n(x,y),\\ y=x ay Q_n(x,y), * where P_n and Q_n are homogeneous polynomials of degree n2, and a R. Consider the functions * &()=P_n() Q_n()\\ &()=Q_n()-P_n()\\ &_1()=a()-(),\\ &_2()=(n-1)(2a()-()) '(). [...]
2018 - 10.1016/j.jde.2018.05.019
Journal of differential equations, Vol. 265, issue 9 (Nov. 2018) , p. 3888-3913  
4.
5 p, 574.4 KB Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We consider a complex differential system with a resonant saddle at the origin. We compute the resonant saddle quantities and using Gröbner bases we find the integrability conditions for such systems up to a certain degree. [...]
2017 - 10.1016/j.chaos.2017.01.014
Chaos, Solitons and Fractals, Vol. 96 (2017) , p. 130-131  
5.
14 p, 708.3 KB On the integrability of the 5-dimensional Lorenz system for the gravity-wave activity / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We consider the 5-dimensional Lorenz system \[ U' &= -V W b V Z, \\ V' &= UW-b UZ, \\ W'&= -U V,\\ X' &= -Z, \\ Z'&=b UV X \] where b \R \0\ and the derivative is with respect to T. [...]
2017
Proceedings of the American Mathematical Society, Vol. 145 Núm. 2 (2017) , p. 665-679  
6.
15 p, 651.1 KB Centers of weight-homogeneous polynomial vector fields on the plane / Giné, Jaume (Universitat de Lleida. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We characterize all centers of a planar weight-homogeneous polynomial vector fields. Moreover we classify all centers of a planar weight-homogeneous polynomial vector fields of degrees 6 and 7.
2017
Proceedings of the American Mathematical Society, Vol. 145 Núm. 6 (2017) , p. 2539-2555  
7.
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  
8.
30 p, 812.6 KB Averaging methods of arbitrary order, periodic solutions and integrability / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Wu, Kesheng (Shanghai Jiao Tong University. Department of Mathematics) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
In this paper we provide an arbitrary order averaging theory for higher dimensional periodic analytic differential systems. This result extends and improves results on averaging theory of periodic analytic differential systems, and it unifies many different kinds of averaging methods. [...]
2016 - 10.1016/j.jde.2015.11.005
Journal of Differential Equations, Vol. 260 (2016) , p. 4130-4156  
9.
50 p, 374.9 KB Limit cycles bifurcating from a degenerate center / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic polynomial differential systems we prove that at most three limit cycles can bifurcate from the degenerate center. [...]
2016 - 10.1016/j.matcom.2015.05.005
Mathematics and Computers in Simulation, Vol. 120 (2016) , p. 1-11  
10.
13 p, 810.8 KB Liouvillian integrability versus Darboux polynomials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
In this note we provide a sufficient condition on the existence of Darboux polynomials of polynomial differential systems via existence of Jacobian multiplier or of Liouvillian first integral and a degree condition among different components of the system. [...]
2016 - 10.1007/s12346-016-0212-1
Qualitative Theory of Dynamical Systems, Vol. 15 (2016) , p. 503-515  

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