Master Dissertation
Document
Master Dissertation
Author
Full name
Gustavo Rodrigues Ferreira
E-mail
Institute/School/College
Instituto de Matemática e Estatística
Program or Specialty
Date of Defense
2019-07-25
Published
São Paulo, 2019
Supervisor
Committee
Lomonaco, Luciana Luna Anna (President)
Bonnot, Sylvain Philippe Pierre
Hazard, Peter Edward
Title in English
Symmetries of Julia sets for analytic endomorphisms of the Riemann sphere
Keywords in English
Dynamical systems, Holomorphic dynamics, Symmetries
Abstract in English
Since the 1980s, much progress has been done in completely determining which functions share a Julia set. The polynomial case was completely solved in 1995, and it was shown that the symmetries of the Julia set play a central role in answering this question. The rational case remains open, but it was already shown to be much more complex than the polynomial one. In this thesis, we review existing results on rational maps sharing a Julia set, and offer results of our own on the symmetry group of such maps.
Title in Portuguese
Simetrias de conjuntos de Julia para endomorfismos analíticos da esfera de Riemann
Keywords in Portuguese
Dinâmica holomorfa, Simetrias, Sistemas dinâmicos
Abstract in Portuguese
Desde a década de oitenta, um enorme progresso foi feito no problema de determinar quais funções têm o mesmo conjunto de Julia. O caso polinomial foi completamente respondido em 1995, e mostrou-se que as simetrias do conjunto de Julia têm um papel central nessa questão. O caso racional permanece aberto, mas já se sabe que ele é muito mais complexo do que o polinomial. Nesta dissertação, nós revisamos resultados existentes sobre aplicações racionais com o mesmo conjunto de Julia e apresentamos nossos próprios resultados sobre o grupo de simetrias de tais aplicações.
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Publishing Date
2019-09-04
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