Generalised dimensions of measures on self-affine sets

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Abstract

We obtain bounds for the generalized q-dimensions of measures supported by self-affine sets that ate valid for 'almost all' families of affine mappings. Exact values are established for self-affine measures and for Gibbs measures when 1 < q less than or equal to 2. These q-dimensions may exhibit phase transitions as q varies.

Original languageEnglish
Pages (from-to)877-891
Number of pages15
JournalNonlinearity
Volume12
Issue number4
DOIs
Publication statusPublished - Jul 1999

Keywords

  • STRANGE ATTRACTORS
  • MULTIFRACTAL FORMALISM
  • HAUSDORFF DIMENSION
  • SIERPINSKI CARPETS
  • FRACTALS
  • SPECTRUM

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