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Resultats globals: 11 registres trobats en 0.03 segons.
Articles, 10 registres trobats
Documents de recerca, 1 registres trobats
Articles 10 registres trobats  
1.
24 p, 449.0 KB Probability of existence of limit cycles for a family of planar systems / Coll, Bartomeu (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
The goal of this work is the study of the probability of occurrence of limit cycles for a family of planar differential systems that are a natural extension of linear ones. To prove our results we first develop several results of non-existence, existence, uniqueness and non-uniqueness of limit cycles for this family. [...]
2023 - 10.1016/j.jde.2023.07.015
Journal of differential equations, Vol. 373 (November 2023) , p. 152-175  
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2.
22 p, 288.8 KB Persistence of periodic traveling waves and Abelian integrals / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Geyer, Anna (Delft University of Technology. Delft Institute of Applied Mathematics) ; Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) is a consequence of the fact that an associated planar ordinary differential equation (ODE) has certain types of solutions defined for all time. [...]
2021 - 10.1016/j.jde.2021.05.033
Journal of differential equations, Vol. 293 (August 2021) , p. 48-69
2 documents
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3.
12 p, 322.1 KB The cyclicity of the period annulus of a reversible quadratic system / Liu, Changjian (Sun Yat-sen University. School of Mathematics (China)) ; Li, Chengzhi (Peking University. School of Mathematical Sciences (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that perturbing the periodic annulus of the reversible quadratic polynomial differential system x˙ = y + ax2, y˙ = −x with a ≠ 0 inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycle, including their multiplicities. [...]
2021 - 10.1017/prm.2021.2
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, (February 2021)  
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4.
13 p, 392.0 KB A Chebyshev criterion with applications / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Geyer, Anna (Delft University of Technology. Delft Institute of Applied Mathematics (The Netherlands)) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We show that a family of certain definite integrals forms a Chebyshev system if two families of associated functions appearing in their integrands are Chebyshev systems as well. We apply this criterion to several examples which appear in the context of perturbations of periodic non-autonomous ODEs to determine bounds on the number of isolated periodic solutions, as well as to persistence problems of periodic solutions for perturbed Hamiltonian systems.
2020 - 10.1016/j.jde.2020.05.015
Journal of differential equations, Vol. 269, Issue 9 (October 2020) , p. 6641-6655  
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5.
21 p, 392.8 KB A new approach for the study of limit cycles / García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Centre national de la recherche scientifique (França). Institut Denis Poisson)
We prove that star-like limit cycles of any planar polynomial system can also be seen either as solutions defined on a given interval of a new associated planar non-autonomous polynomial system or as heteroclinic solutions of a 3-dimensional polynomial system. [...]
2020 - 10.1016/j.jde.2020.04.038
Journal of differential equations, Vol. 269, Issue 7 (September 2020) , p. 6269-6292  
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6.
16 p, 431.6 KB Rational parameterizations approach for solving equations in some dynamical systems problems / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Lázaro, J. Tomás (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We show how the use of rational parameterizations facilitates the study of the number of solutions of many systems of equations involving polynomials and square roots of polynomials. We illustrate the effectiveness of this approach, applying it to several problems appearing in the study of some dynamical systems. [...]
2019 - 10.1007/s12346-018-0300-5
Qualitative theory of dynamical systems, Vol. 18, Issue 2 (August 2019) , p. 583-602  
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7.
24 p, 485.3 KB Poincaré-Pontryagin-Melnikov functions for a class of perturbed planar Hamiltonian equations / Rebollo-Perdomo, Salomón (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we consider polynomial perturbations of a family of polynomial Hamiltonian equations whose associated Hamiltonian is not transversal to infinity, and its complexification is not a Morse polynomial. [...]
2016 - 10.1007/s12346-015-0185-5
Qualitative theory of dynamical systems, 2016  
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8.
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 - 10.1016/j.bulsci.2013.09.004
Bulletin des Sciences Mathematiques, Vol. 138 (2014) , p. 124-138  
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9.
20 p, 399.5 KB Alien limit cycles in Liénard equations / Coll, Bartomeu (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Dumortier, Freddy (Universiteit Hasselt(Belgium). Dept. Wiskunde) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
This paper aims at providing an example of a family of polynomial Liénard equations exhibiting an alien limit cycle. This limit cycle is perturbed from a 2-saddle cycle in the boundary of an annulus of periodic orbits given by a Hamiltonian vector field. [...]
2013 - 10.1016/j.jde.2012.11.005
Journal of differential equations, Vol. 254 (2013) , p. 1582-1600  
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10.
13 p, 408.9 KB Bounding the number of zeros of certain Abelian integrals / Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villadelprat Yagüe, Jordi (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n + k − 1 zeros counted with multiplicities. [...]
2011 - 10.1016/j.jde.2011.05.026
Journal of differential equations, Vol. 251 (2011) , p. 1656-1669  
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Documents de recerca 1 registres trobats  
1.
132 p, 1.2 MB Dois métodos para a investigação de ciclos limites que bifurcam de centros / Rezende, Alex Carlucci ; Oliveira, Regilene Delazari dos Santos, dir.
Um dos mais investigados problemas na teoria qualitativa dos sistemas dinâmicos no plano é o XVI problema de Hilbert que trata dos ciclos limites. Mais precisamente, a segunda parte do referido problema questiona sobre o número máximo de ciclos limites de um sistema diferencial polinomial plano de grau n. [...]
One of the most investigated problems in the qualitative theory of dynamical systems in the plane is the XVI Hilbert's problem which deals with limit cycles. More precisely, the second part of the problem asks about the maximum number of limit cycles of a polynomial differential system of degree n. [...]
2011  
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