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Articles, 19 registres trobats
Articles 19 registres trobats  1 - 10següent  anar al registre:
1.
12 p, 363.9 KB Analytic reducibility of nondegenerate centers: Cherkas systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems x˙ = y, y˙ = P0(x) + P1(x)y + P2(x)y2, where Pi(x) are polynomials of degree n, P0(0) = 0 and P′0(0) < 0. [...]
2016 - 10.14232/ejqtde.2016.1.49
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 49 (2016) , p. 1-10  
2.
30 p, 812.6 KB Averaging methods of arbitrary order, periodic solutions and integrability / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Wu, Kesheng (Shanghai Jiao Tong University. Department of Mathematics) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
In this paper we provide an arbitrary order averaging theory for higher dimensional periodic analytic differential systems. This result extends and improves results on averaging theory of periodic analytic differential systems, and it unifies many different kinds of averaging methods. [...]
2016 - 10.1016/j.jde.2015.11.005
Journal of Differential Equations, Vol. 260 (2016) , p. 4130-4156  
3.
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  
4.
13 p, 810.8 KB Liouvillian integrability versus Darboux polynomials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
In this note we provide a sufficient condition on the existence of Darboux polynomials of polynomial differential systems via existence of Jacobian multiplier or of Liouvillian first integral and a degree condition among different components of the system. [...]
2016 - 10.1007/s12346-016-0212-1
Qualitative Theory of Dynamical Systems, Vol. 15 (2016) , p. 503-515  
5.
11 p, 721.3 KB On the polynomial integrability of a system motivated by the Riemann ellipsoid problem / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We consider differential systems obtained by coupling two Euler–Poinsot systems. The motivation to consider such systems can be traced back to the Riemann ellipsoid problem. We provide new cases for which these systems are completely integrable. [...]
2016 - 10.1051/cocv/2015035
ESAIM. Control, Optimisation and Calculus of Variations, Vol. 22 (2016) , p. 872-882  
6.
6 p, 641.7 KB Analytic integrability of a class of planar polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
In this paper we find necessary and sufficient conditions in order that the differential systems of the form ˙x = xf(y), ˙y = g(y), with f and g polynomials, have a first integral which is analytic in the variable x and meromorphic in the variable y. [...]
2015 - 10.3934/dcdsb.2015.20.2657
Discrete and Continuous Dynamical Systems. Series B, Vol. 20 Núm. 8 (2015) , p. 2657-2661  
7.
14 p, 337.6 KB Local Darboux first integrals of analytic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Walcher, Sebastian ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)
In this paper we discuss local and formal Darboux first integrals of analytic differential systems, using the theory of Poincaré Dulac normal forms. We study the effect of local Darboux integrability on analytic normalization. [...]
2014 - 10.1016/j.bulsci.2013.09.007
Bulletin des Sciences Mathematiques, Vol. 138 (2014) , p. 71-88  
8.
14 p, 706.0 KB Darboux integrability of 2-dimensional Halmiltonian systems with homogeneous potentials of degree 3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We provide a characterization of all Hamiltonian systems of the form H = (p21 + p22)/2 + V (q1, q2) where V is a homogenous polynomial of degree 3 which are completely integrable with Darboux first integrals.
2014 - 10.1063/1.4868701
Journal of Mathematical Physics, Vol. 55 (2014) , p. 33507  
9.
11 p, 614.5 KB Darboux invariants for planar polynomial differential systems having an invariant conic / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Messias, Marcelo (FCT–UNESP(Brazil). Departamento de Matemática e Computacâo) ; Reinol, Alison C. (FCT–UNESP(Brazil). Departamento de Matemática e Computacâo)
We characterize all the planar polynomial differential systems with a unique invariant algebraic curve given by a real conic and having a Darboux invariant.
2014 - 10.1007/s00033-013-0390-5
ZAMP. Journal of Applied Mathematics and Physics, Vol. 65 (2014) , p. 1127-1136  
10.
28 p, 735.5 KB Limit cycles for a generalization of polynomial Liénard differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the number of limit cycles of the polynomial differential systems of the form x˙ = y − f1(x)y, y˙ = −x − g2(x) − f2(x)y, where f1(x) = εf11(x) + ε2f12(x) + ε3f13(x), g2(x) = εg21(x) + ε2g22(x) +ε3g23(x) and f2(x) = εf21(x)+ε2f22(x)+ε3f23(x) where f1i, f2i and g2i have degree l, n and m respectively for each i = 1, 2, 3, and ε is a small parameter. [...]
2013 - 10.1016/j.chaos.2012.11.010
Chaos, Solitons and Fractals, Vol. 46 (2013) , p. 65-74  

Articles : 19 registres trobats   1 - 10següent  anar al registre:
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