数学物理学报(英文版)

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ITERATED FUNCTION SYSTEM AND GALTON-WATSON TREE

余旌胡; 谢南瑞   

  1. 武汉理工大学理学院, 武汉 430070
  • 收稿日期:2005-06-28 修回日期:2005-12-29 出版日期:2007-07-20 发布日期:2007-07-20
  • 通讯作者: 余旌胡
  • 基金资助:

    Both authors are supported by a grant NSC 2002/3-2115-M-002-017.

ITERATED FUNCTION SYSTEM AND GALTON-WATSON TREE

Yu Jinghu; Shieh Narn-Rueih   

  1. Department of Mathematics, School of Natural Sciences,
    Wuhan University of Technology, Wuhan 430070, China
  • Received:2005-06-28 Revised:2005-12-29 Online:2007-07-20 Published:2007-07-20
  • Contact: Yu Jinghu

摘要:

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 $\mu_\o$ supported on
random subset $K_\o$ of $K$, $\mu_\o$ 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].

关键词: Multifraetal structure, iterated function styslem, Galton-Watson tree

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 $\mu_\o$ supported on
random subset $K_\o$ of $K$, $\mu_\o$ 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].

Key words: Multifraetal structure, iterated function styslem, Galton-Watson tree

中图分类号: 

  • 03C57