Abstract
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.
Original language | English |
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Pages (from-to) | 45-96 |
Number of pages | 52 |
Journal | Advances in Mathematics |
Volume | 141 |
Issue number | 1 |
DOIs | |
State | Published - Jan 15 1999 |
Scopus Subject Areas
- General Mathematics
Keywords
- Dimension spectrum
- Multifractal measure
- Self-similarity
- Stopping time
- Strict convexity
- Thermodynamic formalism