A lower bound for the symbolic multifractal spectrum of a self-similar multifractal with arbitrary overlaps
✍ Scribed by L. Olsen
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 238 KB
- Volume
- 282
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
By now the multifractal structure of self‐similar measures satisfying the so‐called Open Set Condition is well understood. However, if the Open Set Condition is not satisfied, then almost nothing is known. In this paper we prove a nontrivial lower bound for the symbolic multifractal spectrum of an arbitrary self‐similar measure. We emphasize that we are considering arbitrary self‐similar measures (and sets) which are not assumed to satisfy the Open Set Condition or similar separation conditions. Our results also have applications to self‐similar sets which do not satisfy the Open Set Condition (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)