On dimensions of multitype Moran sets

Qing Hui Liu*, Zhi Ying Wen

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

16 引用 (Scopus)

摘要

Multitype Moran sets are introduced in this paper. They appear naturally in the study of the structure of the quasi-crystal spectrum, and they generalize some known fractal structures such as self-similar sets, graph-direct sets and Moran sets. It is known that for any Moran set E with a bounded condition on contracting ratios, one has dimH E=s* ≤ s*= dim P E= dimB E, where s* and s* are the lower and upper pre-dimension according to the natural coverings. For any multitype Moran set E with a bounded condition on contracting ratios, we prove dimB E{=}s*. With an additional assumption of primitivity, we prove that for multitype Moran sets, the above formula still holds. We also give some examples to show that if the condition of primitivity is not fulfilled, then it may happen that $\dim_H E or $\dim_P E.

源语言英语
页(从-至)541-553
页数13
期刊Mathematical Proceedings of the Cambridge Philosophical Society
139
3
DOI
出版状态已出版 - 11月 2005

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