Under some technical assumptions it is shown that the Hausdorff dimension of the harmonic measure on the limit set of a conformal infinite iterated function system is strictly less than the Hausdorff dimension of the limit set itself if the limit set is contained in a real-analytic curve, if the ite
Dimensions for random self–conformal sets
✍ Scribed by Yan–Yan Liu; Jun Wu
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 177 KB
- Volume
- 250
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
A set is called regular if its Hausdorff dimension and upper box–counting dimension coincide. In this paper, we prove that the random self–conformal set is regular almost surely. Also we determine the dimensions for a class of random self–conformal sets.
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