Resultados globales: 9 registros encontrados en 0.04 segundos.
Artículos, Encontrados 8 registros
Documentos de investigación, Encontrados 1 registros
Artículos Encontrados 8 registros  
1.
17 p, 362.7 KB A new result on averaging theory for a class of discontinuous planar differential systems with applications / Itikawa, Jackson (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática (Brazil))
We develop the averaging theory at any order for computing the periodic solutions of periodic discontinuous piecewise differential system of the form dr/dθ= r'={F+(θ, r, ϵ) if 0≤ θ ≤ α, F-(θ, r, ϵ) if α ≤ θ ≤ 2π, where F±(θ, r, ϵ) = Σk i=1 ϵiF± i (θ, r) + ϵk+1R ± (θ, r, ϵ) with θ ϵ S and r ϵ D, where D is an open interval of ℝ+, and ϵ is a small real parameter. [...]
2017 - 10.4171/rmi/970
Revista Matemática Iberoamericana, Vol. 33, Issue 4 (2017) , p. 1247-1265  
2.
14 p, 332.1 KB Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones / Itikawa, Jackson (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (Universidade Federal de São Carlos. Departamento de Física, Química e Matemática (Brazil)) ; Oliveira, Regilene D. S. (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil))
We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. [...]
2017 - 10.3934/dcdsb.2017136
Discrete and continuous dynamical systems. Series B, Vol. 22, Issue 9 (November 2017) , p. 3259-3272  
3.
7 p, 285.2 KB New classes of polynomial maps satisfying the real Jacobian conjecture in R2 / Itikawa, Jackson (Universidade Federal de Rondônia. Departamento de Matemática (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ2. The first class is formed by the polynomials maps of the form (q(x) - p(y),q(y) + p(x)): ℝ2 → ℝ2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. [...]
2019 - 10.1590/0001-3765201920170627
Anais da Academia Brasileira de Ciencias, Vol. 91, Issue 2 (2019) , art. e20170627
2 documentos
4.
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  
5.
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  
6.
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  
7.
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  
8.
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  

Documentos de investigación Encontrados 1 registros  
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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