数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1514-1522.doi: 10.1016/S0252-9602(10)60144-0

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IFS ON BOUNDARIES OF HOMOGENEOUS TREES: WQB CONDITION AND MULTIFRACTAC ANALYSIS

刘浩, 文志雄   

  1. School of Mathematics and Statistics, Wuhan University,  |Wuhan 430072, China|School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan   |430074, China
  • 收稿日期:2008-07-21 修回日期:2009-03-15 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    This work was supported by NSFC (10571140).

IFS ON BOUNDARIES OF HOMOGENEOUS TREES: WQB CONDITION AND MULTIFRACTAC ANALYSIS

 LIU Hao, WEN Zhi-Xiong   

  1. School of Mathematics and Statistics, Wuhan University,  |Wuhan 430072, China|School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan   |430074, China
  • Received:2008-07-21 Revised:2009-03-15 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    This work was supported by NSFC (10571140).

摘要:

We study, from the point of view of the multifractal analysis, iterated function systems on totally disconnected spaces, namely, the boundaries of homogeneous trees. In particular, we study in this setting the "weak quasi-Bernoulli'' property introduced by Testud [3, 4]. After projection on R or R2, we get new examples of self-similar measures which, being WQB, obey the multifractal formalism for positive q's.

关键词: IFS, multifractal, quasi-Bernoulli, weak quasi-Bernoulli

Abstract:

We study, from the point of view of the multifractal analysis, iterated function systems on totally disconnected spaces, namely, the boundaries of homogeneous trees. In particular, we study in this setting the "weak quasi-Bernoulli'' property introduced by Testud [3, 4]. After projection on R or R2, we get new examples of self-similar measures which, being WQB, obey the multifractal formalism for positive q's.

Key words: IFS, multifractal, quasi-Bernoulli, weak quasi-Bernoulli

中图分类号: 

  • 28A78