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On the Hausdorff dimension of Cantor-like sets with overlaps

✍ Scribed by Józef Myjak; Tomasz Szarek


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
112 KB
Volume
18
Category
Article
ISSN
0960-0779

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✦ Synopsis


We give a lower estimate of the Hausdorff dimension for Cantor-like sets which are obtained by an overlapping Moran-like construction.


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The Hausdorff Dimension of Sets Arising
✍ Bryan P. Rynne 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 204 KB

Let m, n be positive integers and let : Z n Ä R be a non-negative function. Let W(m, n; ) be the set { X # R mn : " : n j=1 x ij q j " < (q), 1 i m, for infinitely many q # Z n = . The Hausdorff dimension of W(m, n; ) is obtained for arbitrary non-negative functions , with no monotonicity assumpti