González, Set - Search Results - UAB Digital Repository of Documents

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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 - DOI (Digital Object Identifier)

10.3390/axioms12040342
Axioms, Vol. 12, Issue 4 (March 2023) , art. 342

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30 p, 478.1 KB

Center boundaries for planar piecewise-smooth differential equations with two zones / Buzzi, Claudio. (Universidade Estadual Paulista (Brasil). Department of Mathematics) ; Pazim, Rubens (Universidade Federal de Mato Grosso (Brasil). Inst. de Ciências Naturais Humanas e Sociais) ; Pérez-González, Set (Universidade Estadual Paulista (Brasil). Department of Mathematics)
This paper is concerned with 1-parameter families of periodic solutions of piecewise smooth planar vector fields, when they behave like a center of smooth vector fields. We are interested in finding a separation boundary for a given pair of smooth systems in such a way that the discontinuous system, formed by the pair of smooth systems, has a continuum of periodic orbits. [...]
2017 - DOI (Digital Object Identifier)

10.1016/j.jmaa.2016.07.022
Journal of mathematical analysis and applications, Vol. 445 (2017) , p. 631-649

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21 p, 458.8 KB

Existence and uniqueness of limit cycles for generalized -Laplacian Liénard equations / Pérez-González, Set (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torres, Pedro J. (Universidad de Granada. Departamento de Matemática Aplicada)
The Liénard equation x'' + f(x)x' + g(x) = 0 appears as a model in many problems of science and engineering. Since the first half of the 20th century, many papers have appeared providing existence and uniqueness conditions for limit cycles of Li'enard equations. [...]
2016 - DOI (Digital Object Identifier)

10.1016/j.jmaa.2016.03.004
Journal of mathematical analysis and applications, Vol. 439 (2016) , p. 745-765

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15 p, 373.1 KB

Simultaneous bifurcation of limit cycles from a linear center with extra singular points / Pérez-González, Set (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The period annuli of the planar vector field x' = −yF(x, y), y' = xF(x, y), where the set {F(x, y) = 0} consists of k different isolated points, is defined by k + 1 concentric annuli. In this paper we perturb it with polynomials of degree n and we study how many limit cycles bifurcate, up to a first order analysis, from all the period annuli simultaneously in terms of k and n. [...]
2014 - DOI (Digital Object Identifier)

10.1016/j.bulsci.2013.09.004
Bulletin des Sciences Mathematiques, Vol. 138 (2014) , p. 124-138

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117 p, 1.3 MB

On the number of limit cycles for some families of planar differential equations / Pérez-González, Set ; Torregrosa, Joan, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
The results included in this chapter involve an ad hoc compactification designed withtwo objectives. First, to unify the different behaviors of the functions in (4) satisfyingour hypothesis. And second, to make possible the comprehension of the global phaseportrait. [...]
[Barcelona] : Universitat Autònoma de Barcelona, 2012

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