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Articles 26 records found  previous11 - 20next  jump to record: Search took 0.00 seconds. 
11.
20 p, 503.3 KB Univalent wandering domains in the Eremenko-Lyubich class / Fagella Rabionet, Núria (Universitat de Barcelona. Institut de Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Institut de Matemàtiques) ; Lazebnik, Kirill (California Institute of Technology (Estats Units d'Amèrica))
We use the Folding Theorem of [Bis15] to construct an entire function f in class ℬ and a wandering domain U of f such that f restricted to fn (U) is univalent, for all n ≥ 0. The components of the wandering orbit are bounded and surrounded by the postcritical set.
2019 - 10.1007/s11854-027-0079-x
Journal d'Analyse Mathématique, Vol. 139, Issue 1 (October 2019) , p. 369-395  
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12.
21 p, 428.1 KB Escaping points in the boundaries of Baker domains / Barański, 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.
2019 - 10.1007/s11854-019-0011-0
Journal d'Analyse Mathématique, Vol. 137, Issue 2 (March 2019) , p. 679-706  
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13.
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)
Let f be a function in the Eremenko-Lyubich class B, and let U be an unbounded, forward invariant Fatou component of f. We relate the number of singularities of an inner function associated to f $w ith the number of tracts of f. [...]
2019 - 10.1016/j.jmaa.2019.04.045
Journal of mathematical analysis and applications, Vol. 477, Issue 1 (September 2019) , p. 536-550  
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14.
15 p, 8.6 MB Connectivity of Julia sets of Newton maps : a unified approach / Barański, 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 Matemática Iberoamericana, Vol. 34, issue 3 (2018) , p. 1211-1228  
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15.
18 p, 337.6 KB Singular values and bounded Siegel disks / Benini, Anna Miriam (Università di Tor Vergata. Dipartimento di Matematica) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Let f be an entire transcendental function of finite order and Δ be a forward invariant bounded Siegel disk for f with rotation number in Herman's class H. We show that if f has two singular values with bounded orbit, then the boundary of Δ contains a critical point. [...]
2018 - 10.1017/S0305004117000469
Mathematical proceedings of the Cambridge Philosophical Society, Vol. 165, issue 2 (Sep. 2018) , p. 249-265  
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16.
31 p, 7.8 MB Accesses to infinity from Fatou components / Barański, 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  
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17.
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  
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18.
27 p, 2.8 MB Hyperbolic entire functions with bounded Fatou components / Bergweiler, Walter (Christian-Albrechts-Universität zu Kiel (Alemanya)) ; 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  
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19.
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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20.
34 p, 476.4 KB On the connectivity of Julia sets of meromorphic functions / Barański, 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  
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