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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2010.tde-20230727-113512
Document
Author
Full name
Arlane Manoel da Silva e Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2010
Supervisor
Title in Portuguese
Dinâmica de funções transcendentes
Keywords in Portuguese
Funções De Uma Variável Complexa
Funções Inteiras
Abstract in Portuguese
Segundo o Teorema de Baker, as órbitas periódicas repulsoras de uma função inteira transcendente f formam um conjunto denso em J (f). Neste trabalho apresentamos uma prova elementar deste fato, seguindo [5], e outra prova alternativa usando o Teorema das Cinco Ilhas de Ahlfors. Em contraste com a dinâmica de funções racionais, vericamos que, em geral, não vale o Teorema das componentes não-errantes no caso transcendente. No entanto, seguindo [11][14][23][19], provamos que tal resultado pode ser estendido para certas classes de funções inteiras transcendentes.
Title in English
not available
Abstract in English
According to Baker's theorem, the periodic orbits repellers of an entire transcendental map f forms a dense set in J (f). At this work we present an elementary proof of this fact following [5], and other alternative proof using Ahlfors Five Islands Theorem. In contrast to the dynamics of rational maps, we found that, in general, not worth the non-wandering components theorem for entire transcendental maps. However, following [11][14][23][19], we prove that this result can be extended to certain classes of transcendental entire maps.
 
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Publishing Date
2023-07-27
 
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