Separation conditions for conformal iterated function systems
Publication in refereed journal

香港中文大學研究人員

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替代計量分析
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摘要We extend both the weak separation condition and the finite type condition to include finite iterated function systems (IFSs) of injective C(1) conformal contractions on compact subsets of R(d). For conformal IFSs satisfying the bounded distortion property, we prove that the finite type condition implies the weak separation condition. By assuming the weak separation condition, we prove that the Hausdorff and box dimensions of the attractor are equal and, if the dimension of the attractor is a, then its alpha-dimensional Hausdorff measure is positive and finite. We obtain a necessary and sufficient condition for the associated self-conformal measure mu to be singular. By using these we give a first example of a singular invariant measure mu that is associated with a non-linear IFS with overlaps.
著者Lau KS, Ngai SM, Wang XY
期刊名稱Monatshefte für Mathematik
出版年份2009
月份4
日期1
卷號156
期次4
出版社Springer Verlag (Germany)
頁次325 - 355
國際標準期刊號0026-9255
電子國際標準期刊號1436-5081
語言英式英語
關鍵詞Absolute continuity; Conformal iterated function system; Finite type condition; Hausdorff measure; Self-conformal measure; Singularity; Weak separation condition
Web of Science 學科類別Mathematics; MATHEMATICS

上次更新時間 2021-25-02 於 01:28