Results overview: Found 6 records in 0.02 seconds.
Articles, 5 records found
Research literature, 1 records found
Articles 5 records found  
1.
8 p, 341.6 KB Uniform isochronous cubic and quartic centers: Revisited / Artés, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we completed the classification of the phase portraits in the Poincaré disc of uniform isochronous cubic and quartic centers previously studied by several authors. There are three and fourteen different topological phase portraits for the uniform isochronous cubic and quartic centers respectively.
2017 - 10.1016/j.cam.2016.09.018
Journal of Computational and Applied Mathematics, Vol. 313 (2017) , p. 448-453  
2.
13 p, 310.1 KB Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities / Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We classify the global phase portraits in the Poincar\'e disc of the differential systems =-y xf(x,y), =x yf(x,y), where f(x,y) is a homogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. [...]
2016 - 10.3934/dcdsb.2016.21.121
Discrete and Continuous Dynamical Systems. Series B, Vol. 21 Núm. 1 (2016) , p. 121-131  
3.
36 p, 790.3 KB Limit cycles for continuous and discontinuous perturbations of uniform isochronous cubic centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let p be a uniform isochronous cubic polynomial center. We study the maximum number of small or medium limit cycles that bifurcate from p or from the periodic solutions surrounding p respectively, when they are perturbed, either inside the class of all continuous cubic polynomial differential systems, or inside the class of all discontinuous differential systems formed by two cubic differential systems separated by the straight line y = 0. [...]
2015 - 10.1016/j.cam.2014.09.007
Journal of Computational and Applied Mathematics, Vol. 277 (2015) , p. 171-191  
4.
23 p, 433.4 KB Phase portraits of uniform isochronous quartic centers / Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we classify the global phase portraits in the Poincaré disc of all quartic polynomial differential systems with a uniform isochronous center at the origin such that their nonlinear part is not homogeneous.
2015 - 10.1016/j.cam.2015.02.046
Journal of Computational and Applied Mathematics, Vol. 287 (2015) , p. 98-114  
5.
13 p, 609.8 KB Limit cycles bifurcanting from the period annulus of a uniform isochronous center in a quartic polynomial differential system / Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the number of limit cycles that bifurcate from the periodic solutions surrounding a uniform isochronous center located at the origin of the quartic polynomial differential system =-y xy(x^2 y^2), =x y^2(x^2 y^2), when it is perturbed inside the class of all quartic polynomial differential systems. [...]
2015
Electronic Journal of Differential Equations, Vol. 2015 Núm. 246 (2015) , p. 11 pages  

Research literature 1 records found  
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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