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Articles 40 registres trobats  1 - 10següentfinal  anar al registre:
1.
10 p, 567.6 KB On the Bifurcation of Limit Cycles Due to Polynomial Perturbations of Hamiltonian Centers / Colak, Ilker (Drexel University (Texas). Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We study the number of limit cycles bifurcating from the peri- od annulus of a real planar polynomial Hamiltonian ordinary differential system with a center at the origin when it is perturbed in the class of polynomial vector fields of a given degree.
2017 - 10.1007/s00009-017-0857-2
Mediterranean Journal of Mathematics, 2017  
2.
16 p, 437.4 KB Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory / Benterki, Rebiha (Centre Universitaire de Bordj Bou Arréridj(Algeria). Département de Mathématiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4.
2017 - 10.1016/j.cam.2016.08.047
Journal of Computational and Applied Mathematics, Vol. 313 (2017) , p. 273-283  
3.
18 p, 599.5 KB When parallels and meridians are limit cycles for polynomial vector fields on quadrics of revolution in the euclidean 3-space / Dias, Fabio Scalco (Universidade Federal de Itajubá(Brazil). Instituto de Matemática e Computacâo) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mello, Luis Fernando (Universidade Federal de Itajubá(Brazil). Instituto de Matemática e Computacâo)
We study polynomial vector fields of arbitrary degree in R^3 with an invariant quadric of revolution. We characterize all the possible configurations of invariant meridians and parallels that these vector fields can exhibit. [...]
2016 - 10.1142/S0218127416501601
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 26 Núm. 9 (2016) , p. 1650160 (14 pages)  
4.
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  
5.
13 p, 615.6 KB Limit cycles of linear vectors on manifolds / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
It is well known that linear vector fields on the manifold R^n cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C^1 connected manifold.
2016 - 10.1088/0951-7715/29/10/3120
Nonlinearity, Vol. 29 (2016) , p. 3120-3131  
6.
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  
7.
23 p, 542.3 KB Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms / Gouveia, Marcio R. A. (IBILCE–UNESP(Brazil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pessoa, Claudio (IBILCE–UNESP(Brazil). Departamento de Matemática)
We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane \Sigma which admits an invariant hyperplane \Omega transversal to \Sigma containing a period annulus A fulfilled by crossing periodic solutions. [...]
2016 - 10.1016/j.jde.2015.12.034
Journal of Differential Equations, Vol. 260 (2016) , p. 6108-6129  
8.
23 p, 495.5 KB Limit cycles in planar piecewise linear differential systems with nonregular separation line / Cardin, Pedro T. (UNESP(Brazil). Departamento de Matemática) ; Torregrosa Arús, Joan  (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we deal with lanar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles and 2 - respectively, for (0,). [...]
2016 - 10.1016/j.physd.2016.07.008
Physica D. Nonlinear Phenomena, Vol. 337 (2016) , p. 67-82  
9.
12 p, 584.1 KB Limit cycles bifurcating from the periodic annulus of the weight-homogeneous polynomial centers of weight-degree 2 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Lopes, Bruno D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; de Moraes, Jaime R. (IBILCE–UNESP(Brazil). Departamento de Matemática)
We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic polynomial differential systems. [...]
2016 - 10.1016/j.amc.2015.10.079
Applied Mathematics and Computation, Vol. 274 (2016) , p. 47-54  
10.
16 p, 737.1 KB Birth of limit cycles for a classe of continuous and discontinuous differential systems in (d 2)-dimension / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática) ; Zeli, Iris O. (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
The orbits of the reversible differential system ˙x = −y, ˙y = x, ˙z = 0, with x, y ∈ R and z ∈ R d, are periodic with the exception of the equilibrium points (0, 0, z1, . . . , zd). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ˙x = −y, ˙y = x, ˙z = 0, using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree n, and second inside the class of all discontinuous piecewise polynomial differential systems of degree n with two pieces, one in y > 0 and the other in y < 0. [...]
2016 - 10.1080/14689367.2015.1102868
Dynamical Systems. An International Journal, Vol. 31 Núm. 3 (2016) , p. 237-250  

Articles : 40 registres trobats   1 - 10següentfinal  anar al registre:
Documents de recerca 1 registres trobats  
1.
143 p, 889.1 KB Uniform isochronous centers of degrees 3 and 4 and their perturbations / Itikawa, Jackson ; Llibre, Jaume, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
En este trabajo se estudian los sistemas diferenciales polinomiales planos de grado 3 y 4 con un centro isócrono uniforme. Proporcionamos una clasificación para estos sistemas con respecto a la equivalencia topológica de sus retratos de fase globales en el disco de Poincaré. [...]
[Barcelona] : Universitat Autònoma de Barcelona, 2015  

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