Wandering domains and entire maps of bounded type
Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2016, Director: Xavier Jarque i Ribera
| Autor: | |
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/107307 |
| Acceso en línea: | https://hdl.handle.net/2445/107307 |
| Access Level: | acceso abierto |
| Palabra clave: | Sistemes dinàmics complexos Funcions enteres Treballs de fi de màster Complex dynamical systems Entire functions Master's theses |
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Wandering domains and entire maps of bounded typeMalešević Bubenik, AnaSistemes dinàmics complexosFuncions enteresTreballs de fi de màsterComplex dynamical systemsEntire functionsMaster's thesesTreballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2016, Director: Xavier Jarque i RiberaComplex dynamics is one of the richest and most active branches of dynamical systems. Its goal is to study what happens to analytic functions on the complex plane (or the Riemann sphere) when it is iterated. In this master thesis the focus is on transcendental dynamics since the assumption is that $f:\mathbb{C}\rightarrow \mathbb{C}$ is a transcendental entire function. The foundations of complex dynamics were laid by Pierre Fatou and Gaston Julia in the 1920s when they defined the Fatou and Julia sets, named after them. Roughly speaking, the Fatou set is the stable set since all the points in a neighbourhood have the same behaviour after iteration. Alternatively, the points of the Julia set are those that behave unpredictably after iteration. For that reason the Julia set is also called the chaotic set. Both sets are invariant and give a natural partition of the complex plane. The Fatou set is made up of the complementary domains in $\mathbb{C}$ of the Julia set, the Fatou components. Since it is stable a possible Fatou components. Since it is stable a possible Fatou component $U$ can be either periodic (if $f^p(U)=U$ for some $p \in \mathbb{N})$, pre-periodic (if they are periodic eventually) or wandering (if$f^n(U) \cap f^m(U)=\emptyset$ for $m\neq n$).Jarque i Ribera, Xavier2016info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/107307Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc-by-nc-nd (c) Ana Malešević Bubenik, 2016http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1073072026-05-27T06:46:51Z |
| dc.title.none.fl_str_mv |
Wandering domains and entire maps of bounded type |
| title |
Wandering domains and entire maps of bounded type |
| spellingShingle |
Wandering domains and entire maps of bounded type Malešević Bubenik, Ana Sistemes dinàmics complexos Funcions enteres Treballs de fi de màster Complex dynamical systems Entire functions Master's theses |
| title_short |
Wandering domains and entire maps of bounded type |
| title_full |
Wandering domains and entire maps of bounded type |
| title_fullStr |
Wandering domains and entire maps of bounded type |
| title_full_unstemmed |
Wandering domains and entire maps of bounded type |
| title_sort |
Wandering domains and entire maps of bounded type |
| dc.creator.none.fl_str_mv |
Malešević Bubenik, Ana |
| author |
Malešević Bubenik, Ana |
| author_facet |
Malešević Bubenik, Ana |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Jarque i Ribera, Xavier |
| dc.subject.none.fl_str_mv |
Sistemes dinàmics complexos Funcions enteres Treballs de fi de màster Complex dynamical systems Entire functions Master's theses |
| topic |
Sistemes dinàmics complexos Funcions enteres Treballs de fi de màster Complex dynamical systems Entire functions Master's theses |
| description |
Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2016, Director: Xavier Jarque i Ribera |
| publishDate |
2016 |
| dc.date.none.fl_str_mv |
2016 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/masterThesis |
| format |
masterThesis |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/107307 |
| url |
https://hdl.handle.net/2445/107307 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.rights.none.fl_str_mv |
cc-by-nc-nd (c) Ana Malešević Bubenik, 2016 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
cc-by-nc-nd (c) Ana Malešević Bubenik, 2016 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.source.none.fl_str_mv |
Màster Oficial - Matemàtica Avançada reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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1869413061527339008 |
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15,301603 |