Home > Search Results: Barański, Krzysztof
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Articles, 7 records found
Articles 7 records found  
1.
19 p, 594.1 KB Fatou components and singularities of meromorphic functions / Barański, Krzysztof (University of Warsaw. Institute of Mathematics (Poland)) ; Fagella Rabionet, Núria (Universitat de Barcelona. Institut de Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Institut de Matemàtiques) ; Karpińska, Bogusława (Warsaw University of Technology (Poland))
We prove several results concerning the relative position of points in the postsingular set P(f) of a meromorphic map f and the boundary of a Baker domain or the successive iterates of a wandering component. [...]
2020 - 10.1017/prm.2018.142
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 150, Issue 2 (April 2020) , p. 633-654  
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2.
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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3.
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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4.
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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5.
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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6.
20 p, 347.6 KB Absorbing sets and Baker domains for holomorphic maps / 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 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, Vol. 92 Núm. 1 (2014) , p. 144-162  
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7.
19 p, 385.7 KB Brushing the hairs of transcendental entire functions / Barański, Krzysztof (University of Warsaw(Poland). Institute of Mathematics) ; Jarque i Ribera, Xavier (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Rempe, Lasse (University of Liverpool(UK). Department of Mathematical Sciences)
Let f be a transcendental entire function of finite order in the EremenkoLyubich class B (or a finite composition of such maps), and suppose that f is hyperbolic and has a unique Fatou component. We show that the Julia set of f is a Cantor bouquet; i. [...]
2012 - 10.1016/j.topol.2012.02.004
Topology and its applications, Vol. 159 Núm. 8 (2012) , p. 2102-2114  
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7 Baranski, Krzysztof
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