Resultats globals: 22 registres trobats en 0.01 segons.
Articles, 19 registres trobats
Documents de recerca, 3 registres trobats
Articles 19 registres trobats  1 - 10següent  anar al registre:
1.
19 p, 430.8 KB Limit cycles for discontinuous planar piecewise linear differential systems separated by an algebraic curve / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
We study how to change the maximum number of limit cycles of the discontinuous piecewise linear differential systems with only two pieces in function of the degree of the discontinuity of the algebraic curve between the two linear differential systems. [...]
2019 - 10.1142/S0218127419500172
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 29, Núm. 2 (February 2019) , art. 1950017  
2.
17 p, 373.5 KB The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
We provide sufficient conditions for the non-existence, existence and uniqueness of limit cycles surrounding a focus of a quadratic polynomial differential system in the plane.
2019 - 10.1017/S0308210517000221
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, Vol. 149, Issue 1 (February 2019) , p. 1-14  
3.
14 p, 356.4 KB Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles.
2018 - 10.1016/j.jmaa.2018.07.024
Journal of mathematical analysis and applications, Vol. 467, issue 1 (Nov. 2018) , p. 537-549  
4.
21 p, 377.6 KB The number of polynomial solutions of polynomial Riccati equations / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan  (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
Consider real or complex polynomial Riccati differential equations a(x) y=b_0(x) b_1(x)y b_2(x)y^2 with all the involved functions being polynomials of degree at most . We prove that the maximum number of polynomial solutions is 1 (resp. [...]
2016 - 10.1016/j.jde.2016.07.019
Journal of Differential Equations, Vol. 261 (2016) , p. 5071-5093  
5.
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  
6.
13 p, 615.6 KB Limit cycles of linear vectors on manifolds / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
It is well known that linear vector fields on the manifold R^n cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C^1 connected manifold.
2016
Nonlinearity, Vol. 29 (2016) , p. 3120-3131  
7.
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  
8.
25 p, 696.1 KB Darboux integrability and Algebraic limit cycles for a class of polynomial differential Systems / Cao, Jinlong (Shanghai Jiao Tong University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems ˙x = λx − y + Pn+1(x, y) + xF2n(x, y), ˙y = x + λy + Qn+1(x, y)+yF2n(x, y), where Pi(x, y), Qi(x, y) and Fi(x, y) are homogeneous polynomials of degree i. [...]
2014 - 10.1007/s11425-014-4772-8
Science China Mathematics, Vol. 57 Núm. 4 (2014), p. 775-794  
9.
5 p, 607.4 KB On the analytic integrability of the 5-dimensional Lorenz system for the gravitiy-wave activity / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Saghin, Radu (Universitat Autònoma de Barcelona. Centre de Recerca per a l'Educació Científica i Matemàtica) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)
The 5-dimensional Lorenz system for the coupled Rosby and gravity waves has exactly two independent analytic first integrals.
2014 - 10.1090/S0002-9939-2013-11773-9
Proceedings of the American Mathematical Society, Vol. 142 Núm. 2 (2014) , p. 531-537  
10.
14 p, 337.6 KB Local Darboux first integrals of analytic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Walcher, Sebastian (RWTH Aachen(Germany). Lehrstuhl A fur Mathematik) ; 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  

Articles : 19 registres trobats   1 - 10següent  anar al registre:
Documents de recerca 3 registres trobats  
1.
10 p, 187.9 KB Rational first integrals in the Darboux theory of integrability in Cn / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics) ; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
"Vegeu el resum a l'inici del document del fitxer adjunt".
Centre de Recerca Matemàtica 2008 (Prepublicacions del Centre de Recerca Matemàtica ; 789)  
2.
21 p, 263.3 KB Hopf bifurcation in higher dimensional differential systems via the averaging method / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics) ; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
"vegeu el resum a l'inici del document del fitxer adjunt".
Centre de Recerca Matemàtica 2008 (Prepublicacions del Centre de Recerca Matemàtica ; 788)  
3.
18 p, 239.1 KB Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds / Liu, Fei (Shanghai Jiaotong University. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics) ; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
"Vegeu el resum a l'inici del document del fitxer adjunt".
Centre de Recerca Matemàtica 2008 (Prepublicacions del Centre de Recerca Matemàtica ; 787)  

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