Resultats globals: 9 registres trobats en 0.02 segons.
Articles, 9 registres trobats
Articles 9 registres trobats  
1.
14 p, 712.2 KB Liouvillian first integrals for a class of generalized Liénard polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemática)
We study the existence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' =-g(x)-f(x)y, where f(x) = 3Q(x)Q'(x)P(x) + Q(x) P'(x) and g(x) = Q(x)Q'(x)(Q(x) P(x)-1) with P,Q [x]. [...]
2016 - 10.1017/S0308210515000906
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 146, Issue 6 (December 2016) , p. 1195-1210  
2.
19 p, 420.8 KB Phase portraits of continuous piecewise linear Liénard differential systems with three zones / Li, Shimin (Guangdong University of Finance and Economics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Phase portraits are an invaluable tool in studying differential systems. Most of known results about global phase portraits are related to the smooth differential systems. This paper deals with a class of planar continuous piecewise linear Liénard differential systems with three zones separated by two vertical lines without symmetry. [...]
2019 - 10.1016/j.chaos.2018.12.037
Chaos, solitons and fractals, Vol. 120 (March 2019) , p. 149-157  
3.
38 p, 502.2 KB Limit cycles via higher order perturbations for some piecewise differential systems / Buzzi, Claudio. (Universidade Estadual Paulista (Brasil). Department of Mathematics) ; Lima, Mauricio Firmino Silva (Universidade Federal do ABC(Brazil). Centro de Matemática Computacâo e Cognicâo) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x',y')=(-y + εf(x,y,ε),x εg(x,y,ε)). In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. [...]
2018 - 10.1016/j.physd.2018.01.007
Physica D. Nonlinear phenomena, Vol. 371 (May 2018) , p. 28-47  
4.
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 1973- (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  
5.
9 p, 757.4 KB Liouvillian first integrals for generalized Liénard polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' = −g(x) − f(x)y, where g(x) and f(x) are arbitrary polynomials such that 2 ≤ deg g ≤ deg f.
2013 - 10.1515/ans-2013-0404
Advanced Nonlinear Studies, Vol. 13 (2013) , p. 819-829  
6.
10 p, 662.0 KB On the polynomial differential systems having polynomial first integrals / García, Belen (Universidad de Oviedo. Departamento de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Suárez Pérez del Río, Jesús (Universidad de Oviedo. Departamento de Matemáticas)
We consider the class of complex planar polynomial differential systems having a polynomial first integral. Inside this class the systems having minimal polynomial first integrals without critical remarkable values are the Hamiltonian ones. [...]
2012 - 10.1016/j.bulsci.2011.11.003
Bulletin des Sciences Mathematiques, Vol. 136 (2012) , p. 309-316  
7.
10 p, 289.7 KB Weierstrass integrability in Liénard differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work we study the Liénard differential systems that admit a Weierstrass first integral or a Weierstrass inverse integrating factor.
2011 - 10.1016/j.jmaa.2010.11.005
Journal of mathematical analysis and applications, Vol. 377 Núm. 1 (2011) , p. 362-369  
8.
6 p, 729.4 KB Limit cycles of a class of generalized Liénard polynomial equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Makhlouf, Ammar (University of Annaba (Algeria). Department of Mathematics)
We prove that the generalized Liénard polynomial differential system x'=y^2p-1, y'=-x^2q-1 - f(x) y^2n-1, where p, q, and n are positive integers; is a small parameter; and f(x) is a polynomial of degree m which can have [m/2] limit cycles, where [x] is the integer part function of x.
2015 - 10.1007/s10883-014-9253-4
Journal of Dynamical and Control Systems, Vol. 21 (2015) , p. 189-192  
9.
10 p, 720.5 KB The generalized Liénard polynomial differential systems x'=y,y'= -g(x) - f (x)y with deg g = deg f 1 are not Liouvillian integrable / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Instituto Superior Técnico. Departamento de Matemática)
We prove the nonexistence of Liouvillian first integrals for the generalized Li\'enard polynomial differential systems of the form x' = y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that g = f 1.
2015 - 10.1016/j.bulsci.2014.08.010
Bulletin des Sciences Mathematiques, Vol. 139 (2015) , p. 214-227  

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