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
No coin nor oath required. For personal study only.
✦ Synopsis
We give a lower estimate of the Hausdorff dimension for Cantor-like sets which are obtained by an overlapping Moran-like construction.
📜 SIMILAR VOLUMES
Facult e e de pharmacie and Centre de recherches math e ematiques, Universit e e de Montr e eal, C.P. 6128, Succ. Centre-ville, Montr e eal (Qu e ebec), Canada H3C 3J7
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
proved that for 0 \* 1 the set where W$(t) is a standard Wiener process. A corresponding result is obtained when W$ is replaced by a two-parameter Wiener process.