Results overview: Found 16 records in 0.02 seconds.
Articles, 14 records found
Research literature, 2 records found
Articles 14 records found  1 - 10next  jump to record:
1.
21 p, 428.1 KB Escaping points in the boundaries of Baker domains / Baranski, Krzysztof (University of Warsaw (Polònia). Institute of Mathematics) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica) ; Karpinska, Boguslawa (University of Warsaw (Polònia). Institute of Mathematics)
We study the dynamical behaviour of points in the boundaries of simply connected invariant Baker domains U of meromorphic maps f with a finite degree on U. We prove that if f $u is of hyperbolic or simply parabolic type, then almost every point in the boundary ofU,with respect to harmonicmeasure, escapes to infinity under iteration of f. [...]
2019 - 10.1007/s11854-019-0011-0
Journal d'Analyse Mathématique, Vol. 137, Issue 2 (March 2019) , p. 679-706  
2.
17 p, 411.0 KB Singularities of inner functions associated with hyperbolic maps / Evdoridou, Vasiliki (The Open University) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica) ; Sixsmith, David J. (University of Liverpool)
2019 - 10.1016/j.jmaa.2019.04.045
Journal of mathematical analysis and applications, Vol. 477, Issue 1 (September 2019) , p. 536-550  
3.
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  
4.
31 p, 7.8 MB Accesses to infinity from Fatou components / 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 (Warsaw University of Technology (Polònia). Faculty of Mathematics and Information Science)
We study the boundary behaviour of a meromorphic map f: \C C on its invariant simply connected Fatou component U. To this aim, we develop the theory of accesses to boundary points of U and their relation to the dynamics of f. [...]
2017
Transactions of the American Mathematical Society, Vol. 369 Núm. 3 (2017) , p. 1835-1867  
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.
27 p, 2.8 MB Hyperbolic entire functions with bounded Fatou components / Bergweiler, Walter (Christian-Albrechts-Universität zu Kiel(Germany). Mathematisches Seminar) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Rempe, Lasse (University of Liverpool(UK). Dept. of Mathematical Sciences)
We show that an invariant Fatou component of a hyperbolic transcendental entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. [...]
2015
Commentarii Mathematici Helvetici. A Journal of the Swiss Mathematical Society, Vol. 90 Núm. 4 (2015) , p. 799-829  
7.
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. Series A I. Mathematica, Vol. 39 (2014) , p. 3-22  
8.
34 p, 476.4 KB On the connectivity of Julia sets of meromorphic functions / Baranski, Krzysztof (University of Warsaw(Poland). 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 (Warsaw University of Technology(Poland). Faculty of Mathematics and Information Science)
We prove that every transcendental meromorphic map f with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. [...]
2014 - 10.1007/s00222-014-0504-5
Inventiones Mathematicae, Vol. 198 Núm. 3 (2014) , p. 591-636  
9.
20 p, 347.6 KB Absorbing sets and Baker domains for holomorphic maps / Baranski, Krzysztof (University of Warsaw(Poland). 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 (Warsaw University of Technology(Poland). Faculty of Mathematics and Information Science)
We consider holomorphic maps f: U U for a hyperbolic domain U in the complex plane, such that the iterates of f converge to a boundary point of U. By a previous result of the authors, for such maps there exist nice absorbing domains W U. [...]
2014 - 10.1112/jlms/jdv016
Journal of the London Mathematical Society. Second Series, Vol. 92 Núm. 1 (2014) , p. 144-162  
10.
17 p, 1.1 MB On the configuration of Herman rings of meromorphic functions / Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi) ; Peter, Jorn (Christian-Albrechts-Universität zu Kiel(Germany). Mathematisches Seminar)
We prove some results concerning the possible configurations of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period and give a sufficient condition for a configuration to be realizable.
2012 - 10.1016/j.jmaa.2012.05.005
Journal of Mathematical Analysis and Applications, Vol. 394 (2012) , p. 458-467  

Articles : 14 records found   1 - 10next  jump to record:
Research literature 2 records found  
1.
132 p, 26.4 MB On a family of degree 4 Blaschke products / Canela Sánchez, Jordi ; Fagella Rabionet, Núria, dir. ; Garijo, Antoni, dir. ; Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi
[Barcelona] : Universitat de Barcelona, 2015  
2.
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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