A new exact method for obtaining the multifractal spectrum of multiscaled multinomial measures and IFS invariant measures
✍ Scribed by J.M. Gutiérrez; M.A. Rodrı́guez
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 285 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0960-0779
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✦ Synopsis
In this paper we present a new exact method for obtaining the multifractal spectrum of multiscaled multinomial measures and invariant measures associated with iterated function systems (IFS). A multinomial measure is shown to be generated as the invariant measure of an associated IFS. Then, the multifractal spectrum of the measure is determined by a couple of parametric implicit equations. This analysis generalizes some results previously obtained for the case of single-scaled multinomial measures (e.g., the binomial measure). A geometric interpretation of this new framework working in the space of codes of the IFS gives new insight into the nature of the multifractal formalism.