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1.
32 p, 619.7 KB Periodic orbits and nonintegrability of the Henon-Heiles Hamiltonian systems / Lembarki, Fatima Ezzahra ; Llibre, Jaume, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
Dans la nature et dans la vie des hommes, de nombreux processus, sont en constante évolution. Nous parlons donc de systèmes dynamiques. Généralement ces changements incessants sont souvent difficiles à prédire et modéliser car ils surviennent de manière non linéaire et n’obéissent pas pleinement aux simples lois du hasard.
2011  

Articles 71 registres trobats  1 - 10següentfinal  anar al registre:
1.
28 p, 723.4 KB Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory / Lembarki, Fatima Ezzahra ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide sufficient conditions on the energy levels to guarantee the existence of periodic orbits for the perturbed elliptic oscillators in 6D using the averaging theory. We give also an analytical estimation of the shape of these periodic orbits parameterized by the energy. [...]
2016 - 10.1007/s10509-016-2930-x
Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, 2016, p. 361-340  
2.
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  
3.
12 p, 680.4 KB New results on averaging theory and applications / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i. [...]
2016 - 10.1007/s00033-016-0682-7
ZAMP. Journal of Applied Mathematics and Physics, Vol. 67:106 (2016) , p. 11p.  
4.
12 p, 1.7 MB New families of periodic orbits for a galactic potential / de Bustos, Maria T. (Universidad de Salamanca. Departamento de Matemática Aplicada) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; Vera, Juan A. (Universidad Politécnica de Cartagena. Centro Universitario de la Defensa)
The Hamiltonian system associated to the Hamiltonian \[ H=(P_1^2 P_2^2 P_3^2)/2 (Q_1^2 Q_2^2 Q_3^2)/2 (Q_1^4 Q_2^4 Q_3^4 a(Q_1^2Q_2^2 Q_1^2Q_3^2 Q_2^2Q_3^2)), \] where and a are parameters and is small, describes the local motion in the central area of a galaxy. [...]
2016 - 10.1016/j.chaos.2015.11.003
Chaos, Solitons and Fractals, Vol. 82 (2016) , p. 97-102  
5.
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  
6.
16 p, 818.1 KB Polynomial and linearized normal forms for almost periodic differential systems / Li, Weigu (Peking University. School of Mathematical Sciences) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Wu, Hao (Peking University. School of Mathematical Sciences)
For almost periodic differential systems ˙x = εf(x, t, ε) with x ∈ Cn, t ∈ R and ε > 0 small enough, we get a polynomial normal form in a neighborhood of a hyperbolic singular point of the system ˙x = ε limT→∞1T∫ T0f(x,t, 0) dt, if its eigenvalues are in the Poincaré domain. [...]
2016 - 10.3934/dcds.2016.36.345
Discrete and Continuous Dynamical Systems. Series A, Vol. 36 Núm. 1 (2016) , p. 345-360  
7.
25 p, 401.8 KB Limit cycles coming from some uniform isochronous centers / Liang, Haihua (Guangdong Polytechnic Normal University(China). Department of Computer Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa Arús, Joan  (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
This article is about the weak 16--th Hilbert problem, i. e. we analyze how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems. [...]
2016 - 10.1515/ans-2015-5010
Advanced Nonlinear Studies, Vol. 16 Núm. 2 (2016) , p. 197-220  
8.
23 p, 689.0 KB Periodic motion in perturbed elliptic oscillators revisited / Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We analytically study the Hamiltonian system in R^4 with Hamiltonian H= 12 (p_x^2 p_y^2) 12 (_1^2 x^2 _2^2 y^2)- V_1(x,y) being (a) V_1(x,y)=-(xy^2 ax^3) and (b) V_1(x,y)=-(x^2y ax^3) with aR, where is a small parameter and _1 and _2 are the unperturbed frequencies of the oscillations along the x and y axis, respectively. [...]
2016 - 10.1007/s10509-016-2927-5
Astrophysics and Space Science. An International Journal of Astronomy, Astrophysics and Space Science, Vol. 361:348 (2016) , p. 1-8  
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  

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