UAB Digital Repository of Documents 17 records found  1 - 10next  jump to record: Search took 0.00 seconds. 
1.
27 p, 521.7 KB Some results on homoclinic and heteroclinic connections in planar systems / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Université de Tours. Laboratoire de Mathématiques et Physique Théorique (France)) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Consider a family of planar systems depending on two parameters (n, b) and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when Φ(n, b) = 0. [...]
2010 - 10.1088/0951-7715/23/12/001
Nonlinearity, Vol. 23, Issue 12 (December 2010) , p. 2977-3001  
2.
A Bendixson-Dulac theorem for some piecewise systems / da Cruz, Leonardo P. C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The Bendixson-Dulac Theorem provides a criterion to find upper bounds for the number of limit cycles in analytic differential systems. We extend this classical result to some classes of piecewise differential systems. [...]
2020 - 10.1088/1361-6544/ab6812
Nonlinearity, Vol. 33, Num. 5 (May 2020) , p. 2455-2480  
3.
Global dynamics of the real secant method / Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
We investigate the root finding algorithm given by the secant method applied to a real polynomial p as a discrete dynamical system defined on R2. We study the shape and distribution of the basins of attraction associated to the roots of p, and we also show the existence of other stable dynamics that might affect the efficiency of the algorithm. [...]
2019 - 10.1088/1361-6544/ab2f55
Nonlinearity, Vol. 32, Issue 11 (November 2019) , p. 4557-4578  
4.
26 p, 414.4 KB New lower bounds for the Hilbert numbers using reversible centers / Prohens, Rafel (Universitat de les Illes Balears. Departament de Matemàtiques i Informàtica) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we provide the best lower bounds, that are known up to now, for the Hilbert numbers of polynomial vector fields of degree N,, for small values of N. These limit cycles appear bifurcating from symmetric Darboux reversible centers with very high simultaneous cyclicity. [...]
2019 - 10.1088/1361-6544/aae94d
Nonlinearity, Vol. 32, Núm. 1 (January 2019) , p. 331-355  
5.
28 p, 445.8 KB Periodic oscillators, isochronous centers and resonance / Ortega, Rafael (Universidad de Granada. Departamento de Matemática Aplicada) ; Rojas, David (Universidad de Granada. Departamento de Matemática Aplicada)
An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. [...]
2019 - 10.1088/1361-6544/aaee9a
Nonlinearity, Vol. 32, Núm. 3 (March 2019) , p. 800-832  
6.
23 p, 801.7 KB On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations / García, Isaac A. (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Maza, Susanna (Universitat de Lleida. Departament de Matemàtica)
In this work we improve the classical averaging theory applied to -families of analytic T-periodic ordinary differential equations in standard form defined on R. First we characterize the set of points z_0 in the phase space and the parameters where T-periodic solutions can be produced when we vary a small parameter . [...]
2018 - 10.1088/1361-6544/aab592
Nonlinearity, Vol. 31, issue 6 (2018) , p. 2666-2688  
7.
31 p, 573.9 KB Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction / Cândido, Murilo R. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universidade Estadual de Campinas (Brasil). Departamento de Matemática)
2017 - 10.1088/1361-6544/aa7e95
Nonlinearity, Vol. 30 Núm. 9 (2017) , p. 3560-3586  
8.
36 p, 2.3 MB Tongues in Degree 4 Blaschke Products / Canela Sánchez, Jordi (Inst. of Math. Polish Academy of Sciences(Poland)) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
The goal of this paper is to investigate the family of Blasche products B_a(z)=z^3-a1- which is a rational family of perturbations of the doubling map. We focus on the tongue-like sets which appear in its parameter plane. [...]
2016
Nonlinearity, Vol. 29 (2016) , p. 3464-3495  
9.
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  
10.
15 p, 424.0 KB Higher order averaging theory for finding periodic solutions via Brouwer degree / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
In this paper we deal with nonlinear differential systems of the form x'(t) = Xki=0εiFi(t, x) + εk+1R(t, x, ε), where Fi : R × D → Rn for i = 0, 1, · · · , k, and R : R × D × (−ε0, ε0) → Rn are continuous functions, T-periodic in the first variable, being D an open subset of Rn, and ε a small parameter. [...]
2014
Nonlinearity, Vol. 27 (2014) , p. 563-583  

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