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2000 mathematics subject classification: primary 37f10 (1) 1
30d05 (1) 1
30d20 (1) 1
37f10 (1) 1
37f10, 30d20 (1) 1
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Inventiones mathematicae, ISSN 0020-9910, 12/2014, Volume 198, Issue 3, pp. 591 - 636
...Invent. math. (2014) 198:591–636 DOI 10.1007/s00222-014-0504-5 On the connectivity of the Julia sets of meromorphic functions Krzysztof Bara ´ nski · Núria... 
30D20 | Primary 30D05 | Mathematics, general | 37F10 | Mathematics | MATHEMATICS | ITERATION | NEWTONS METHOD | MAPS | DYNAMICS | BAKER DOMAINS | ANALYTIC-FUNCTIONS | Discs | Absorption | Mathematical analysis | Newton methods | Texts | Disks | Meromorphic functions | Boundaries | Mathematics - Dynamical Systems | Funcions enteres | Functions of complex variables | Entire functions | Funcions de variables complexes
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 2019, Volume 150, Issue 2, pp. 633 - 654
... Krzysztof Barański Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland (baranski@mimuw.edu.pl) Núria Fagella and Xavier Jarque... 
wandering domain | transcendental dynamics | Baker domain | Julia set | ITERATION | MATHEMATICS, APPLIED | EXAMPLES | WANDERING DOMAINS | JULIA SETS | MATHEMATICS | LIMIT FUNCTIONS | CONNECTIVITY | DYNAMICS | Domains | Disks | Meromorphic functions | Maps | Mathematics - Dynamical Systems | Sistemes dinàmics complexos | Funcions meromorfes | Funcions enteres | Entire functions | Complex dynamical systems
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 2017, Volume 37, Issue 6, pp. 3123 - 3160
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2017, Volume 369, Issue 3, pp. 1835 - 1867
We study the boundary behaviour of a meromorphic map f: \mathbb{C} \to \widehat {\mathbb{C}} on its simply connected invariant Fatou component U. To this aim,... 
MATHEMATICS | NEWTONS METHOD | BOUNDARIES | TREES | MEROMORPHIC FUNCTIONS | ENTIRE MAPS | ATTRACTING BASINS | Mathematics - Dynamical Systems
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 02/2015, Volume 110, Issue 2, pp. 291 - 324
We study the distribution of periodic points for a wide class of maps, namely entire transcendental functions of finite order and with bounded set of singular... 
MATHEMATICS | DYNAMICS | SIEGEL DISKS | POINTS | Theorems | Separation | Maps | Mathematical analysis | Disks | Landing | Formulas (mathematics) | Invariants | Mathematics - Dynamical Systems | Transcendental functions | Funcions transcendents
Journal Article
Nonlinearity, ISSN 0951-7715, 09/2016, Volume 29, Issue 11, pp. 3464 - 3495
The goal of this paper is to investigate the family of Blasche products B-a(z) = z(3) z-a/1-(a) over barz , which is a rational family of perturbations of the... 
circle maps | Blaschke products | tongues | holomorphic dynamics | MATHEMATICS, APPLIED | SET | DOUBLE-STANDARD MAPS | BIFURCATIONS | PHYSICS, MATHEMATICAL | CIRCLE | FAMILY | DYNAMICS | ARNOLD TONGUES | TIP | Mathematics - Dynamical Systems | Dinàmica topològica | Topological dynamics | Differentiable dynamical systems | Sistemes dinàmics diferenciables
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2015, Volume 429, Issue 1, pp. 478 - 496
C. Bishop in [10, Theorem 17.1] constructs an example of an entire function f in class B with at least two grand orbits of oscillating wandering domains. In... 
Entire maps | Quasiconformal maps | Wandering domains | Holomorphic dynamics | MATHEMATICS | ITERATION | MATHEMATICS, APPLIED | DYNAMICS | EXAMPLES | Ergodic theory | Funcions enteres | Polynomials | Teoria ergòdica | Entire functions | Polinomis
Journal Article
Revista Matematica Iberoamericana, ISSN 0213-2230, 2018, Volume 34, Issue 3, pp. 1211 - 1228
In this paper we present a unified proof of the fact that the Julia set of Newton's method applied to a holomorphic function on the complex plane (a polynomial... 
Newton's method | Root-finding algorithm | Iteration | Julia set | MATHEMATICS | REPELLING FIXED-POINTS | DYNAMICS | iteration | BAKER DOMAINS | root-finding algorithm | WANDERING DOMAINS | TRANSCENDENTAL MEROMORPHIC MAPS
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 477, Issue 1, pp. 536 - 550
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... 
Inner functions | Transcendental dynamics | Hyperbolic functions
Journal Article
JOURNAL D ANALYSE MATHEMATIQUE, ISSN 0021-7670, 10/2019, Volume 139, Issue 1, pp. 369 - 395
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 f(n)(U) is... 
MATHEMATICS | LIMIT FUNCTIONS | Domains | Entire functions
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2012, Volume 394, Issue 2, pp. 458 - 467
We prove some results concerning the possible configurations of Herman rings for transcendental meromorphic functions. We show that one pole is enough to... 
Herman rings | Configuration | Complex dynamical systems | Fatou set | Julia set | Quasiconformal surgery | Invariant curves | MATHEMATICS | MATHEMATICS, APPLIED | EXAMPLES | DOMAINS | Ergodic theory | Functions of complex variables | Teoria ergòdica | Funcions de variables complexes
Journal Article
Journal of Geometric Analysis, ISSN 1050-6926, 07/2017, Volume 27, Issue 3, pp. 2381 - 2399
We study the geometric structure of the boundary of Herman rings in a model family of Blaschke products of degree 3 (up to quasiconformal deformation).... 
Holomorpphic dynamics | Herman rings | Julia set | Self-similarity | JULIA SETS | MATHEMATICS | ITERATION | DYNAMICS | SIEGEL DISKS | SIMILARITY | ANALYTIC-FUNCTIONS | Mathematics - Dynamical Systems
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 08/2015, Volume 21, Issue 8, pp. 715 - 741
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2015, Volume 90, Issue 4, pp. 799 - 829
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 3/2019, Volume 137, Issue 2, pp. 679 - 706
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... 
Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS | Information science | Auks | Mathematics - Dynamical Systems
Journal Article
Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2014, Volume 39, Issue 1, pp. 3 - 22
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 8/2007, Volume 273, Issue 3, pp. 755 - 783
... of λz m exp(z) for m ≥ 2 null Núria Fagella 1 , Antonio Garijo 2 1 Dep. de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via de les Corts Catalanes... 
Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Physics | Statistical Physics | Complexity
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2015, Volume 90, Issue 4, p. 799
Journal Article
Journal of the London Mathematical Society, ISSN 1469-7750, 2015, Volume 92, Issue 1, pp. 144 - 162
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 ζ of U. By a... 
MATHEMATICS | ITERATION | NEWTONS METHOD | ANALYTIC-FUNCTIONS | Absorption | Maps | Planes | Mathematical analysis | Classification | Boundaries | Formulas (mathematics) | Lift | Mathematics - Dynamical Systems
Journal Article
ISSN 0308-2105, 07/2018
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... 
Sistemes dinàmics complexos | Funcions analítiques | Funcions enteres | Functional equations | Analytic functions | Entire functions | Complex dynamical systems | Funcions meromorfes | Polynomials | Meromorphic functions | Equacions funcionals | Polinomis
Journal Article
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