Multifractal spectra of in-homogenous self-similar measures

L. Olsen, N. Snigireva

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

Let S-i : R-d -> R-d for i = 1,...,N be contracting similarities. Also, let (P-1, - - -, P-N, P) be a probability vector and let nu be a probability measure on R-d with compact support. Then there exists a unique probability measure mu on R-d such that

mu = Sigma P-i(i)mu circle S-i(-1) + P nu

The mesure mu is called an in-homogenous self-similar measure.

Original languageEnglish
Pages (from-to)1789-1844
Number of pages56
JournalIndiana University Mathematics Journal
Volume57
Issue number4
DOIs
Publication statusPublished - 2008

Keywords

  • multifractals
  • multifractal spectra
  • L-q spectra
  • in-homogenous self-similar measure
  • in-homogenous self-similar set
  • self-similar measure
  • ITERATED FUNCTION SYSTEMS
  • BERNOULLI CONVOLUTIONS
  • PHASE-TRANSITIONS
  • DELETED DIGITS
  • FRACTALS
  • FORMALISM
  • EXPANSIONS
  • DIMENSIONS

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