UAB Digital Repository of Documents 16 records found  1 - 10next  jump to record: Search took 0.02 seconds. 
1.
14 p, 314.2 KB Periodic orbits for the perturbed planar circular restricted 3–body problem / Abouelmagd, Elbaz I. (National Research Institute of Astronomy and Geophysics (Egipte). Astronomy Department) ; Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena (Múrcia). Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We characterize when the classical first and second kind of periodic orbits of the planar circular restricted 3–body problem obtained by Poincaré, can be extended to perturbed planar circular restricted 3–body problems. [...]
2019 - 10.3934/dcdsb.2019003
Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 3 (March 2019) , p. 1007-1020  
2.
17 p, 408.6 KB Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tang, Yilei (Shanghai Jiao Tong University. School of Mathematical Sciences)
We apply the averaging theory of high order for computing the limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. These discontinuous piecewise differential systems are formed by two either quadratic, or cubic polynomial differential systems separated by a straight line. [...]
2019 - 10.3934/dcdsb.2018236
Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 4 (April 2019) , p. 1769-1784  
3.
33 p, 10.7 MB Periodic orbits of perturbed non-axially symmetric potentials in 1:1:1 and 1:1:2 resonances / Corbera Subirana, Montserrat (Universitat de Vic. Departament d'Enginyeries) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
2018 - 10.3934/dcdsb.2018101
Discrete and continuous dynamical systems. Series B, Vol. 23, issue 6 (Aug. 2018) , p. 2299-2337  
4.
13 p, 709.8 KB Algebraic limit cycles for quadratic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We prove that for a quadratic polynomial differential system having three pairs of diametrally opposite equilibrium points at infinity that are positively rationally independent, has at most one algebraic limit cycle. [...]
2018 - 10.3934/dcdsb.2018070
Discrete and continuous dynamical systems. Series B, Vol. 23, issue 6 (2018) , p. 2475-2485  
5.
36 p, 1.2 MB Linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the y-axis / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martinez Mancilla, Yohanna Paulina (Universidad del Bío-Bío. Departamento de Matemática) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
We provide normal forms and the phase portraits in the Poincaré disk for all the linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the y-axis.
2018 - 10.3934/dcdsb.2018047
Discrete and continuous dynamical systems. Series B, Vol. 23, issue 2 (2018) , p. 887-912  
6.
15 p, 328.5 KB Averaging approach to cyclicity of Hopf bifurcation in planar linear-quadratic polynomial discontinuous differential systems / Chen, Xingwu (Sichuan University (Xina). Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Weinian (Sichuan University (Xina). Department of Mathematics)
It is well known that the cyclicity of a Hopf bifurcation in continuous quadratic polynomial differential systems in \R^2 is 3. In contrast here we consider discontinuous differential systems in \R^2 defined in two half--planes separated by a straight line. [...]
2017 - 10.3934/dcdsb.2017203
Discrete and Continuous Dynamical Systems. Series B, Vol. 22 Núm. 10 (2017) , p. 3953-3965  
7.
7 p, 266.0 KB Periodic solutions of some classes of continuous second-order differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba (Algèria). Department of Mathematics)
We study the periodic solutions of the second--order differential equations of the form x x^n = f(t), or x.
2017 - 10.3934/dcdsb.2017022
Discrete and Continuous Dynamical Systems. Series B, Vol. 22 Núm. 2 (2017) , p. 477-482  
8.
9 p, 334.3 KB Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vidal, Claudio (Universidad del Bio Bio (Chile). Departamento de Matemática)
A ratio–dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point E ∗ at the positive octant is unstable. [...]
2016 - 10.3934/dcdsb.2016026
Discrete and Continuous Dynamical Systems. Series B, Vol. 21 Núm. 6 (2016) , p. 1859-1867  
9.
17 p, 333.9 KB On the analytic integrability of the Liénard analytic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We consider the Liénard analytic differential systems x = y, y =-g(x) -f(x)y, where f,g: R R are analytic functions and the origin is an isolated singular point. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the origin and the existence of global analytic first integrals.
2016 - 10.3934/dcdsb.2016.21.557
Discrete and Continuous Dynamical Systems. Series B, Vol. 21 Núm. 2 (2016) , p. 557-573  
10.
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  

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