27 citations · 190 across the 27 of their papers we have counts for
33 papers
On the parameter space of fibered hyperbolic polynomials
Robert Florido, Núria Fagella
We present an application of quasiconformal (QC) surgery for holomorphic maps fibered over an irrational rotation of the unit circle, also known as quasiperiodically forced (QPF) m…
Bifurcation for families of Ahlfors island maps
Matthieu Astorg, Anna Miriam Benini, Nuria Fagella
We extend Mañé-Sad-Sullivan and Lyubich's equivalent characterization of stability to the setting of Ahlfors island maps, which include notably all meromorphic maps. As a consequen…
Shrinking targets and recurrent behaviour for forward compositions of inner functions
Anna Miriam Benini, Vasiliki Evdoridou, Núria Fagella +2
We prove sharp results about recurrent behaviour of orbits of forward compositions of inner functions, inspired by fundamental results about iterates of inner functions, and give e…
Dynamics of projectable functions: Towards an atlas of wandering domains for a family of Newton maps
Robert Florido, Núria Fagella
We present a one-parameter family of transcendental entire functions with zeros, whose Newton's method yields wandering domains, coexisting with the basins of the roots of $F…
Local connectivity of boundaries of tame Fatou components of meromorphic functions
Krzystof Barański, Núria Fagella, Xavier Jarque +1
We prove local connectivity of the boundaries of invariant simply connected attracting basins for a class of transcendental meromorphic maps. The maps within this class need not be…
Boundary dynamics in unbounded Fatou components
Anna Jové, Núria Fagella
We study the behaviour of a transcendental entire map on an unbounded invariant Fatou component , assuming that infinity is accessible from…
Boundary dynamics for holomorphic sequences, non-autonomous dynamical systems and wandering domains
Anna Miriam Benini, Vasiliki Evdoridou, Núria Fagella +2
There are many classical results, related to the Denjoy--Wolff Theorem, concerning the relationship between orbits of interior points and orbits of boundary points under iterates o…
A model for boundary dynamics of Baker domains
Núria Fagella, Anna Jové-Campabadal
We consider the transcendental entire function , which has a doubly parabolic Baker domain of degree two, i.e. an invariant stable component for which all iter…
Dynamical mechanism behind ghosts unveiled in a map complexification
Jordi Canela, Lluís Alsedà, Núria Fagella +1
Complex systems such as ecosystems, electronic circuits, lasers or chemical reactions can be modelled by dynamical systems which typically experience bifurcations. Transients typic…
Bifurcation loci of families of finite type meromorphic maps
Matthieu Astorg, Anna Miriam Benini, Núria Fagella
We show that stability is open and dense in natural families of meromorphic maps of one complex variable with a finite number of singular values, and even more generally, to f…
Classifying simply connected wandering domains
Anna Miriam Benini, Vasiliki Evdoridou, Núria Fagella +2
While the dynamics of transcendental entire functions in periodic Fatou components and in multiply connected wandering domains are well understood, the dynamics in simply connected…
A bound on the number of rationally invisible repelling orbits
Anna Miriam Benini, Núria Fagella
We consider entire transcendental maps with bounded set of singular values such that periodic rays exist and land. For such maps, we prove a refined version of the Fatou-Shishikura…
Singular values and non-repelling cycles for entire transcendental maps
Anna Miriam Benini, Núria Fagella
Let be a map with bounded set of singular values for which periodic dynamic rays exist and land. We prove that each non-repelling cycle is associated to a singular orbit which…
Univalent Wandering Domains in the Eremenko-Lyubich Class
Núria Fagella, Xavier Jarque, Kirill Lazebnik
We use the folding theorem of Bishop to construct an entire function in class and a wandering domain of such that restricted to is univalent, for all $…
Fatou components and singularities of meromorphic functions
Krzysztof Barański, Núria Fagella, Xavier Jarque +1
We prove several results concerning the relative position of points in the postsingular set of a meromorphic map and the boundary of a Baker domain or the successive ite…
Stable components in the parameter plane of transcendental functions of finite type
Nuria Fagella, Linda Keen
We study the parameter planes of certain one-dimensional, dynamically-defined slices of holomorphic families of entire and meromorphic transcendental maps of finite type. Our plane…
Dynamic rays of bounded-type transcendental self-maps of the punctured plane
Núria Fagella, David Martí-Pete
We study the escaping set of functions in the class , that is, holomorphic functions for which both zero and infinity are essential sing…
Escaping points in the boundaries of Baker domains
Krzysztof Barański, Núria Fagella, Xavier Jarque +1
We study the dynamical behaviour of points in the boundaries of simply connected invariant Baker domains of meromorphic maps with a finite degree on . We prove that if $…
The Fine Structure of Herman Rings
Núria Fagella, Christian Henriksen
We study the geometric structure of the boundary of Herman rings in a model family of Blaschke products of degree 3. Shishikura's quasiconformal surgery relates the Herman ring to…
Tongues in Degree 4 Blaschke Products
Jordi Canela, Núria Fagella, Antonio Garijo
The goal of this paper is to investigate the family of Blasche products , which is a rational family of perturbations of the doubling map. We focu…
Connectivity of Julia sets of Newton maps: A unified approach
Krzysztof Barański, Núria Fagella, Xavier Jarque +1
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…
On a Family of Rational Perturbations of the Doubling Map
Jordi Canela, Núria Fagella, Antonio Garijo
The goal of this paper is to investigate the parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products $B_a(z)=z^3\frac{z-a}{1-\bar{a…
Accesses to infinity from Fatou components
Krzysztof Barański, Núria Fagella, Xavier Jarque +1
We study the boundary behaviour of a meromorphic map on its invariant simply connected Fatou component . To this aim, we develop the theor…
Wandering domains for composition of entire functions
Núria Fagella, Sébastien Godillon, Xavier Jarque
C. Bishop has constructed an example of an entire function f in Eremenko-Lyubich class with at least two grand orbits of oscillating wandering domains. In this paper we show that h…