Abstract
For the class of self-similar measures in Rd with overlaps that are essentially of finite type, we set up a framework for deriving a closed formula for the Lq-spectrum of the measure for q ≥ 0 . This framework allows us to include iterated function systems that have different contraction ratios and those in higher dimension. For self-similar measures with overlaps, closed formulas for the Lq-spectrum have only been obtained earlier for measures satisfying Strichartz's second-order identities. We illustrate how to use our results to prove the differentiability of the Lq-spectrum, obtain the multifractal dimension spectrum, and compute the Hausdorff dimension of the measure.
Original language | English |
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Pages (from-to) | 56-103 |
Number of pages | 48 |
Journal | Journal of the Australian Mathematical Society |
Volume | 106 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1 2019 |
Scopus Subject Areas
- General Mathematics
Keywords
- essentially of finite type
- fractal
- L -spectrum
- multifractal formalism
- self-similar measure