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Title: Dynamics on the boundary of Fatou components
Author: Jové Campabadal, Anna
Director/Tutor: Fagella Rabionet, Núria
Keywords: Teoria ergòdica
Sistemes dinàmics complexos
Treballs de fi de màster
Funcions meromorfes
Ergodic theory
Complex dynamical systems
Master's theses
Issue Date: 28-Jun-2021
Abstract: [en] The aim of this project is to compile the known results about the dynamics on the boundary of invariant simply-connected Fatou components, as well as the questions which are still open concerning the topic. We focus on ergodicity and recurrence. One of the main tools to deal with this kind of questions is to study the boundary behaviour of the associate inner functions. Therefore, the project is divided in two parts. Firstly, ergodicity and recurrence are studied for inner functions. Secondly, these results are applied to study the dynamics on the boundary of invariant simply-connected Fatou components. Moreover, we study the concrete example $f(z)=z+e^{-z}$, which presents infinitely many invariant doubly-parabolic Baker domains $U_{k}$. Making use of the associate inner function, which can be computed explicitly, we give a complete characterization of the periodic points in $\partial U_{k}$ and prove the existence of uncountably many curves of non-accessible escaping points.
Note: Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2021, Director: Núria Fagella Rabionet
Appears in Collections:Màster Oficial - Matemàtica Avançada

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