Carregant...
Fitxers
Tipus de document
Treball de fi de grauData de publicació
Llicència de publicació
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/177617
The Denjoy-Wolff theorem, extensions and applications
Títol de la revista
Autors
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
[en] The aim of this project is to prove the Denjoy-Wolff Theorem, which deals with iteration of holomorphic self-maps of the unit disk D. It claims that either the map is conjugate to a rotation about the origin or all the points converge to a unique point in D under iteration. We will also prove that there always exists a fundamental set, an invariant subset reached by all the compact sets in a finite number of iterations and where the map is one-to-one. Fundamental sets can be classified in four different types, up to conformal conjugation.
Finally, we will use this results to classify the periodic Fatou components of entire maps. For each of them, we can find a fundamental set. In the case of attracting or parabolic components or Siegel disks, the dynamics in the fundamental set is determined up to conformal conjugation. However, in the case of Baker domains three different types can occur and we will present some examples of them.
Descripció
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Núria Fagella Rabionet
Citació
Col·leccions
Citació
JOVÉ CAMPABADAL, Anna. The Denjoy-Wolff theorem, extensions and applications. [consulta: 11 de gener de 2026]. [Disponible a: https://hdl.handle.net/2445/177617]