Iterated function system and Galton-Watson tree

作者：Yu, Jinghu^*; Shieh, Narn-Rueih

来源：Acta Mathematica Scientia, 2007, 27(3): 456-464.

DOI：10.1016/S0252-9602(07)60046-0

• multifraetal structure
• iterated function styslem
• Galton-Watson tree

Given a system {S-1,center dot center dot center dot, S-N} 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 it, supported on random subset K-omega of K, mu(omega) 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 Morters-Shieh [12].

• 出版日期2007-7
• 单位武汉理工大学