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Articles, 11 records found
Articles 11 records found  1 - 10next  jump to record:
1.
22 p, 2.1 MB On the basins of attraction of a one-dimensional family of root finding algorithms : from Newton to Traub / Canela Sánchez, Jordi (Universitat Jaume I. Institut Universitari de Matemátiques i Aplicacions de Castelló) ; Evdoridou, Vasiliki (The Open University. School of Mathematics and Statistics (UK)) ; Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
In this paper we study the dynamics of damped Traub's methods T when applied to polynomials. The family of damped Traub's methods consists of root finding algorithms which contain both Newton's (δ= 0) and Traub's method (δ= 1). [...]
2023 - 10.1007/s00209-023-03215-8
Mathematische Zeitschrift, Vol. 303, Issue 3 (March 2023) , art. 55  
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2.
25 p, 1.5 MB Achievable connectivities of Fatou components for a family of singular perturbations / Canela Sánchez, Jordi (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica) ; Paraschiv, Dan (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
In this paper we study the connectivity of Fatou components for maps in a large family of singular perturbations. We prove that, for some parameters inside the family, the dynamical planes for the corresponding maps present Fatou components of arbitrarily large connectivity and we determine precisely these connectivities. [...]
2022 - 10.3934/dcds.2022051
Discrete and continuous dynamical systems. Series A, Vol. 42, Issue 9 (September 2022) , p. 4237-4261  
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3.
20 p, 5.8 MB Singular perturbations of Blaschke products and connectivity of Fatou components / Canela Sánchez, Jordi (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló)
2017 - 10.3934/dcds.2017153
Discrete and continuous dynamical systems. Series A, Vol. 37, Issue 7 (July 2017) , p. 3567-3585  
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4.
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  
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5.
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 Matemàtiques i Informàtica) ; Villadelprat Yagüe, 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  
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6.
13 p, 906.5 KB Newton's method for symmetric quartic polynomials / Campos, Beatriz (Universitat Jaume I. 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. 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  
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7.
21 p, 1.2 MB On McMullen-like mappings / Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Godillon, Sebastién (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
We introduce a generalization of the McMullen family f_(z) = z^n /zd^. In 1988 C. McMullen showed that the Julia set of f_ is a Cantor set of circles if and only if 1/n 1/d < 1 and the simple critical values of f_ belong to the trap door. [...]
2015
Journal of Fractal Geometry, Vol. 2 (2015) , p. 249-279  
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8.
19 p, 1.5 MB Sierpinski curve Julia sets for quadratic rational maps / Devaney, Robert L. (Boston University. Department of Mathematics) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; 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)
We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpi ́nski curve.
2014 - 10.5186/aasfm.2014.3903
Annales Academiae Scientiarum Fennicae. Mathematica, Vol. 39 (2014) , p. 3-22  
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9.
22 p, 3.0 MB Newton's method on Bring-Jerrard polynomials / Campos, Beatriz (Universitat Jaume I. 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. 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 matemàtiques, Vol. Extra (2014) , p. 81-109
2 documents
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10.
27 p, 474.1 KB On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points II / 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) ; Taixés, Jordi (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Following the attracting and preperiodic cases ([5]), in this paper we prove the existence of weakly repelling fixed points for transcendental meromorphic maps, provided that their Fatou set contains a multiply-connected parabolic basin. [...]
2011 - 10.4064/fm215-2-5
Fundamenta Mathematicae, Vol. 215 (2011) , p. 177-202  
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