Iterated function system and Galton-Watson tree
Resource
Acta Mathematica Scientia 27 (3): 456-464
Journal
Acta Mathematica Scientia
Pages
456-464
Date Issued
2007
Date
2007
Author(s)
Yu, J.
Shieh, Narn-Rueih
Abstract
Given a system {S1,...,SN} of N contractive similarities satisfying some strong separation condition, it has an invariant set K for the system. In this article, the authors construct some random measure μω supported on random subset Kω of K, μω having some "non-standard" multifractal structure, which contrasts the well-known multifractal formalism for the invariant measure of system {S1,...,SN} may possess. The main tool is the multifractal structures of a Galton-Watson tree, which are obtained by Liu [9], Shieh-Taylor [14], and Mörters-Shieh [12]. © 2007 Wuhan Institute of Physics and Mathematics.
Type
journal article
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