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Articles 39 registres trobats  1 - 10següentfinal  anar al registre:
1.
Polynomial differential systems with hyperbolic limit cycles / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
One of the main problems of the qualitative theory of the planar differential equations is the study their limit cycles. In this paper given an algebraic curve of degree n we characterize the planar polynomial differential systems of degree greater or equal than n which admit the ovals of the algebraic curve as hyperbolic limit cycles.
2023 - 10.1016/j.geomphys.2023.104983
Journal of geometry and physics, Vol. 194 (December 2023) , art. 104983  
2.
35 p, 627.1 KB Criteria on the existence of limit cycles in planar polynomial differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Grau, Maite (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We summarize known criteria for the non-existence, existence and on the number of limit cycles of autonomous real planar polynomial differential systems, and also provide new results. We give examples of systems which realize the maximum number of limit cycles provided by each criterion. [...]
2022 - 10.1016/j.exmath.2022.09.002
Expositiones Mathematicae, Vol. 40, Issue 4 (December 2022) , p. 1049-1083  
3.
19 p, 397.7 KB Limit Cycles of Polynomially Integrable Piecewise Differential Systems / García, Belén (Universidad de Oviedo. Departamento de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pérez del Río, Jesús S. (Universidad de Oviedo. Departamento de Matemáticas) ; Pérez-González, Set (Universidad de Oviedo. Departamento de Matemáticas)
In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. [...]
2023 - 10.3390/axioms12040342
Axioms, Vol. 12, Issue 4 (March 2023) , art. 342  
4.
6 p, 623.5 KB Polynomial differential systems with even degree have no global centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
Let x˙=P(x,y), y˙=Q(x,y) be a differential system with P and Q real polynomials, and let d=max⁡{degP,degQ}. A singular point p of this differential system is a global center if R2∖{p} is filled with periodic orbits. [...]
2021 - 10.1016/j.jmaa.2021.125281
Journal of mathematical analysis and applications, Vol. 503, Issue 1 (November 2021) , art. 125281  
5.
18 p, 798.2 KB A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, X. (Shanghai Jiao Tong University. School of Mathematical Sciences and MOE-LSC (People's Republic of China))
In the qualitative theory of differential equations in the plane one of the most difficult objects to study is the existence of limit cycles. There are many papers dedicated to this subject. Here we will present a survey mainly dedicated to the algebraic and explicit non-algebraic limit cycles of the polynomial differential systems in R and of the discontinuous piecewise differential systems in R formed by two linear differential systems separated by a straight line. [...]
2021 - 10.1016/j.exmath.2020.03.001
Expositiones Mathematicae, Vol. 39, Issue 1 (March 2021) , p. 48-61  
6.
18 p, 698.2 KB The center problem for the class of Λ- Ω differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The center problem, i. e. distinguish between a focus and a center, is a classical problem in the qualitative theory of planar differential equations which go back to Darboux, Poincaré and Liapunov. [...]
2020 - 10.1007/s12215-020-00568-5
Rendiconti del Circolo Matematico di Palermo, vol. 70 (October 2020) p. 1483-1499  
7.
30 p, 951.8 KB On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Xiao, Dongmei (Shanghai Jiao Tong University. School of Mathematical Sciences (China))
We study the kind of centers that Hamiltonian Kolmogorov cubic polynomial differential systems can exhibit. Moreover, we analyze the possible configurations of these centers with respect to the invariant coordinate axes, and obtain that the real algebraic curve xy(a+bx+cy+dx2+exy+fy2)=h has at most four families of level ovals in R2 for all real parameters a,b,c,d,e,f and h.
2020 - 10.2140/pjm.2020.306.611
Pacific Journal of Mathematics, Vol. 306, Issue 2 (2020) , p. 611-644  
8.
14 p, 336.3 KB On the centers of cubic polynomial differential systems with four invariant straight lines / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Assume that a cubic polynomial differential system in the plane has four invariant straight lines in generic position, i. e. they are not parallel and no more than two straight lines intersect in a point. [...]
2020 - 10.12775/TMNA.2020.004
Topological Methods in Nonlinear Analysis, Vol. 55, Issue 2 (June 2020) , p. 387-402  
9.
16 p, 279.8 KB Linear type global centers of cubic Hamiltonian systems symmetric with respect to the x-axis / Barreira, Luis (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
A polynomial differential system of degree 2 has no global centers (that is, centers defined in all the plane except the fixed point). In this paper we characterize the global centers of cubic Hamiltonian systems symmetric with respect to the x-axis, and such that the center has purely imaginary eigenvalues.
2020
Electronic journal of differential equations, Vol. 2020 Núm. 57 (2020) , p. 1-14
2 documents
10.
31 p, 575.7 KB Limit cycles of piecewise polynomial perturbations of higher dimensional lineal differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática (Brazil)) ; Zeli, Iris O. (Instituto Tecnológico de Aeronáutica. Departamento de Matemática (Brazil))
The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed non-autonomous n-dimensional discontinuous piecewise smooth differential system. [...]
2020 - 10.4171/rmi/1131
Revista Matemática Iberoamericana, Vol. 36, Núm. 1 (2020) , p. 291-318  

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