Multifractal measures and a weak separation condition

Ka Sing Lau, Sze Man Ngai

Research output: Contribution to journalArticlepeer-review

173 Scopus citations

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 languageEnglish
Pages (from-to)45-96
Number of pages52
JournalAdvances in Mathematics
Volume141
Issue number1
DOIs
StatePublished - Jan 15 1999

Scopus Subject Areas

  • General Mathematics

Keywords

  • Dimension spectrum
  • Multifractal measure
  • Self-similarity
  • Stopping time
  • Strict convexity
  • Thermodynamic formalism

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