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Articles 42 registres trobats  1 - 10següentfinal  anar al registre:
1.
18 p, 334.8 KB Limit cycles of linear vector fields on (S2)m ×Rn / Cufí Cabré, Clara (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
It is well known that linear vector fields defined in Rn cannot have limit cycles, but this is not the case for linear vector fields defined in other manifolds. We study the existence of limit cycles bifurcating from a continuum of periodic orbits of linear vector fields on manifolds of the form (S2)m × Rn when such vector fields are perturbed inside the class of all linear vector fields. [...]
2023 - 10.2140/pjm.2023.324.249
Pacific Journal of Mathematics, Vol. 324, Issue 2 (June 2023) , p. 249-263  
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2.
17 p, 375.4 KB Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres / Buzzi, Claudio (Universidade Estadual Paulista Julio de Mesquita Filho. Departamento de Matemática) ; Carvalho, Yagor Romano (Universidade de São Paulo. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
These last years an increasing interest appeared in studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. The understanding of the dynamics of these systems has many difficulties. [...]
2022 - 10.1080/14689367.2022.2122779
Dynamical Systems, Vol. 37, Issue 4 (2022) , p. 710-728  
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3.
15 p, 350.7 KB The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems / Barkat, Meriem (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj. Department of Mathematics) ; Benterki, Rebiha (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In order to understand the dynamics of the planar differential systems, the limit cycles play a main role, but in general their study is not easy. These last years, an increasing interest appeared for studying the limit cycles of some classes of piecewise differential systems, due to the rich applications of this kind of differential systems. [...]
2023 - 10.1007/s11071-022-07891-9
Nonlinear Dynamics, Vol. 111, Issue 2 (January 2023) , p. 1475-1484  
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4.
45 p, 594.9 KB Limit Cycles of piecewise-continuous differential systems formed by linear and quadratic isochronous centers II / Ghermoul, Bilal (University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Salhi, Tayeb (University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria))
We study the crossing periodic orbits and limit cycles of the planar piecewise-continuous differential systems separated by the straight-line x = 0 having in x > 0 the general quadratic isochronous center ẋ = -y + x2, y˙ = x(1 + y) after an affine transformation, and in x < 0 an arbitrary quadratic isochronous center except for the quadratic isochronous center ẋ = -y + x2 - y2, y˙ = x(1 + 2y) which has been studied in [Ghermoul et al. [...]
2022 - 10.1142/S0218127422500912
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 6 (May 2022) , art. 2250091  
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5.
39 p, 573.8 KB Limit cycles of continuous piecewise differential systems formed by linear and quadratic isochronous centers I / Ghermoul, Bilal (University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Salhi, Tayeb (University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria))
First, we study the planar continuous piecewise differential systems separated by the straight line x = 0 formed by a linear isochronous center in x > 0 and an isochronous quadratic center in x < 0. [...]
2022 - 10.1142/S0218127422500031
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 1 (January 2022) , art. 2250003  
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6.
13 p, 663.8 KB Phase portraits of uniform isochronous centers with homogeneous nonlinearities / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
We classify the phase portraits in the Poincaré disc of the differential equations of the form x' = − y + xf(x, y), ẏ = x + yf(x, y) where f(x,y) is a homogeneous polynomial of degree n − 1 when n = 2, 3, 4, 5, and f has only simple zeroes. [...]
2021 - 10.1007/s10883-021-09529-2
Journal of Dynamical and Control Systems, Vol. 28 (February 2021) , p. 319-332  
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7.
17 p, 674.0 KB The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems / Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide the maximum number of limit cycles of some classes of discontinuous piecewise differential systems formed by two differential systems separated by a straight line, when these differential systems are linear centers or three families of cubic isochronous centers, giving rise to ten different classes of discontinuous piecewise differential systems. [...]
2020 - 10.1007/s11071-020-06045-z
Nonlinear Dynamics, Vol. 102, Issue 4 (December 2020) , p. 2453-2466  
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8.
13 p, 273.4 KB Quadratic perturbations of a quadratic reversible Lotka-Volterra system / Li, Chengzhi (Peking University. School of Mathematical Sciences (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that perturbing the two periodic annuli of the quadratic polynomial reversible Lotka-Volterra differential system ̇x = -y + x2 - y2, ẏ = x(1 + 2y), inside the class of all quadratic polynomial differential systems we can obtain the following configurations of limit cycles (0,0), (1,0), (2,0), (1,1) and (1,2).
2010 - 10.1007/s12346-010-0026-5
Qualitative theory of dynamical systems, Vol. 9, Issue 1-2 (November 2010) , p. 235-249  
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9.
10 p, 277.6 KB Chini equations and isochronous centers in three-dimensional differential systems / Chamberland, Marc (Grinnell College. Department of Mathematics and Statistics (USA)) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the number of limit cycles of T -periodic Chini equations and some generalized Abel equations and apply the results obtained to illustrate the existence of isochronous centers in three-dimensional autonomous differential systems.
2010 - 10.1007/s12346-010-0019-4
Qualitative theory of dynamical systems, Vol. 9, Issue 1-2 (November 2010) , p. 29-38  
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10.
19 p, 499.4 KB Bifurcation of critical periods from Pleshkan's isochrones / Grau, Maite (Universitat de Lleida. Departament de Matemàtica) ; Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Pleshkan proved in 1969 that, up to a linear transformation and a constant rescaling of time, there are four isochrones in the family of cubic centers with homogeneous nonlinearities ℓ3. In this paper we prove that if we perturb any of these isochrones inside ℓ3, then at most two critical periods bifurcate from its period annulus. [...]
2010 - 10.1112/jlms/jdp062
Journal of the London Mathematical Society, Vol. 81, Issue 1 (February 2010) , p. 142-160  
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Articles : 42 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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