Results overview: Found 10 records in 0.02 seconds.
Articles, 9 records found
Research literature, 1 records found
Articles 9 records found  
1.
23 p, 5.9 MB Rational maps with Fatou components of arbitrarily large connectivity / Canela Sánchez, Jordi (Université Paul Sabatier. Institut de Mathématiques de Toulouse)
We study the family of singular perturbations of Blaschke products B_a,(z)=z^3-a1- ^2. We analyse how the connectivity of the Fatou components varies as we move continuously the parameter . We prove that all possible escaping configurations of the critical point c_-(a,) take place within the parameter space. [...]
2018 - 10.1016/j.jmaa.2018.01.061
Journal of mathematical analysis and applications, Vol. 462, issue 1 (June 2018) , p. 35-56  
2.
15 p, 8.6 MB Connectivity of Julia sets of Newton maps : a unified approach / Baranski, Krzysztof (University of Warsaw (Polònia). Institute of Mathematics) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Karpinska, Boguslawa (University of Warsaw (Polònia). Institute of Mathematics)
In this paper we give a unified proof of the fact that the Julia set of Newton's method applied to a holomorphic function of the complex plane (a polynomial of degree large than 1 or an entire transcendental function) is connected. [...]
2018 - 10.4171/RMI/1022
Revista Mathemática Iberoamericana, Vol. 34, issue 3 (2018) , p. 1211-1228  
3.
15 p, 3.0 MB An effective algorithm to compute Mandelbrot sets in parameter planes / Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtica i Informàtica) ; Villadelprat, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
In 2000 McMullen proved that copies of generalized Mandelbrot set are dense in the bifurcation locus for generic families of rational maps. We develop an algo- rithm to an effective computation of the location and size of these generalized Mandelbrot sets in parameter space. [...]
2017 - 10.1007/s11075-017-0270-8
Numerical Algorithms, Vol. 76 (2017) , p. 555-571  
4.
13 p, 906.5 KB Newton's method for symmetric quartic polynomials / Campos, Beatriz (Universitat Jaume I(Castelló de la Plana). Departament de Matemàtiques) ; Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier  (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Vindel, Pura (Universitat Jaume I(Castelló de la Plana). Departament de Matemàtiques)
We investigate the parameter plane of the Newton's method applied to the family of quartic polynomials p_a,b(z)=z^4 az^3 bz^2 az 1, where a and b are real parameters. We divide the parameter plane (a,b) R^2 into twelve open and connected regions where p, p' and p'' have simple roots. [...]
2016 - 10.1016/j.amc.2016.06.021
Applied Mathematics and Computation, Vol. 290 (2016) , p. 326-335  
5.
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  
6.
22 p, 3.0 MB Newton's method on Bring-Jerrard polynomials / Campos, Beatriz (Universitat Jaume I (Castelló de la Plana). Departament de Matemàtiques) ; Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Vindel, Pura (Universitat Jaume I (Castelló de la Plana). Departament de Matemàtiques)
In this paper we study the topology of the hyperbolic component of the parameter plane for the Newton's method applied to n-th degree Bring-Jerrard polynomials given by P_n(z) = z^n-cz 1, \ c. For n=5, using the Tschirnhaus-Bring-Jerrard nonlinear transformations, this family controls, at least theoretically, the roots of all quintic polynomials. [...]
2014 - 10.5565/PUBLMAT_Extra14_05
Publicacions Matematiques, Vol. Extra (2014) , p. 81-109
2 documents
7.
21 p, 637.0 KB Wandering domains for composition of entire functions / Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Godillon, Sebastién (Universitat de Barcelona. Institut de Matemàtiques) ; Jarque i Ribera, Xavier (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
C. ~Bishop constructs an example of an entire function f in class B with at least two grand orbits of oscillating wandering domains. In this paper we show that his example has exactly two such orbits, that is, f has no unexpected wandering domains. [...]
2015 - 10.1016/j.jmaa.2015.04.020
Journal of Mathematical Analysis and Applications, Vol. 429 (2015) , p. 478-496  
8.
30 p, 1.8 MB On a Family of Rational Perturbations of the Doubling Map / Canela Sánchez, Jordi (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; 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 parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products. First we study the basic properties of these maps such as the connectivity of the Julia set as a function of the parameter a. [...]
2015 - 10.1080/10236198.2015.1050387
Journal of Difference Equations and Applications, Vol. 21 Núm. 8 (2015) , p. 715-741  
9.
12 p, 216.2 KB Algebraic webs invariant under endomorphisms / Dabija, Marius (University of Michigan. Department of Mathematics) ; Jonsson, Mattias (University of Michigan. Department of Mathematics)
We classify noninvertible, holomorphic selfmaps of the projective plane that preserve an algebraic web. In doing so, we obtain interesting examples of critically finite maps.
2010 - 10.5565/PUBLMAT_54110_07
Publicacions Matemàtiques, V. 54 n. 1 (2010) p. 137-148  

Research literature 1 records found  
1.
112 p, 4.9 MB Connectivity of Julia sets of transcendental meromorphic functions / Taixés i Ventosa, Jordi ; Fagella Rabionet, Núria, dir. (Universitat de Barcelona. Grup de Sistemes Dinàmics) ; Jarque i Ribera, Xavier, dir. (Universitat de Barcelona)
Newton's method associated to a complex holomorphic function f is defined by the dynamical system Nf(z) = z – f(z) / f'(z). As a root-finding algorithm, a natural question is to understand the dynamics of Nf about its fixed points, as they correspond to the roots of the function f. [...]
[Barcelona] : Universitat de Barcelona 2011  

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