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Multifractal Measures and a Weak Separation Condition

✍ Scribed by Ka-Sing Lau; Sze-Man Ngai

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
442 KB
Volume
141
Category
Article
ISSN
0001-8708

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✦ Synopsis

We define a new separation property on the family of contractive similitudes that allows certain overlappings. This property is weaker than the open set condition of Hutchinson. It includes the well-known class of infinite Bernoulli convolutions associated with the P.V. numbers and the solutions of the two-scale dilation equations. Our main purpose in this paper is to prove the multifractal formalism under such condition.

πŸ“œ SIMILAR VOLUMES

A new exact method for obtaining the mul
A new exact method for obtaining the multifractal spectrum of multiscaled multinomial measures and IFS invariant measures
✍ J.M. GutiΓ©rrez; M.A. RodrΔ±́guez πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 285 KB

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 mult