Made available in DSpace on 2014-12-17T15:14:47Z (GMT). No. of bitstreams: 1 DarlanAM.pdf: 1159480 bytes, checksum: d201bf0e3558be6b14b14c9a86a46f20 (MD5) Previous issue date: 2005-03-10 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / In this work we have studied the problem of percolation in a multifractal geometric support, in its different versions, and we have analysed the conection between this problem and the standard percolation and also the connection with the critical phenomena formalism. The projection of the multifractal structure into the subjacent regular lattice allows to map the problem of random percolation in the multifractal lattice into the problem of correlated percolation in the regular lattice. Also we have investigated the critical behavior of the invasion percolation model in this type of environment. We have discussed get the finite size effects / Nesta disserta??o estudamos o problema da percola??o num suporte geom?trico multifractal, em suas diferentes vers?es, e analisamos a conex?o deste problema com a percola??o convencional e com o formalismo dos fen?menos cr?ticos. A proje??o da estrutura multifractal numa rede regular subjacente permite mapear o problema da percola??o aleat?ria no multifractal num problema de percola??o correlacionada numa rede regular. Tamb?m investigamos o comportamento cr?tico do modelo da percola??o por invas?o neste tipo de ambiente e discutimos a quest?o do efeito de tamanho finito