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Doctoral Thesis
Full name
Marcos Yamaguti
Knowledge Area
Date of Defense
São Paulo, 1997
Prado, Carmen Pimentel Cintra do (President)
Caldas, Ibere Luiz
Carneiro, Carlos Eugenio Imbassahy
Curado, Evaldo Mendonca Fleury
Felicio, Jose Roberto Drugowich de
Title in Portuguese
Caracterização Multifractal
Keywords in Portuguese
Box counting
Caos determinístico
Mecânica estatística
Abstract in Portuguese
A caracterização estática dos sistemas caóticos clássicos dissipativos tem sido realizada através do cálculo das dimensões generalizadas 'D IND. q' e do espectro de singularidades f(alfa). Os métodos mais comuns de cálculo numérico dessas funções utilizam algoritmos de contagem de caixa. Porém, esses algoritmos produzem um erro sistemático através de 'caixas espúrias', levando a resultados distorcidos. Por essa razão, estudamos métodos numéricos que não utilizam o algoritmo de contagem de caixa, verificando em que casos eles podem ser aplicados eficazmente e propusemos um novo algoritmo de contagem de caixa que reduz o número de 'caixas espúrias', obtendo melhores resultados.
Title in English
Multifractal characterization
Keywords in English
Box counting
Deterministic chaos
Statistical mechanics
Abstract in English
The static caracterization of classical dissipative chaotical systems has been achieved by the calculation of the generalized dimensions 'D IND. q' and the spectrum of singularities f(alfa). The most used numerical methods of evaluating these functions are based on box counting algorithms. The results obtained by those methods are distorced by the presence of 'spurious boxes' generated intrinsecally by these algorithms. For this reason, we have studied numerical methods that don't use box counting algorithms, and we have tried to verify in which kind of sets they give best results. We also have proposed a new box counting algorithm that reduces the number of 'spurious boxes', and led to better results.
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WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • YAMAGUTI, M., and PRADO, C. P. C. A Direct Calculation Of The Spectrum Of Singularities F(Alfa) Of Multifractals. Modern Physics Letters A, 1995, vol. 206, nº 5-6, p. 318-322.
  • YAMAGUTI, M., and PRADO, C. P. C. Smart Covering For A Box-Counting Algorithm. Physical Review E - Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics, 1997, vol. 55, nº 6, p. 7726-7732.
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