Self-affine multifractal Sierpinski sponges in Rd

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Abstract

We study self-affine multifractals in R-d using the formalism introduced in [Olsen, A multifractal formalism, Advances in Mathematics, 116 (1996), 82-196]. We prove that new multifractal phenomena, not exhibited by self-similar multifractals in R-d, appear in the self-affine case.

Original languageEnglish
Pages (from-to)143-200
Number of pages57
JournalPacific Journal of Mathematics
Volume183
Issue number1
DOIs
Publication statusPublished - Mar 1998

Keywords

  • HAUSDORFF DIMENSION
  • STRANGE ATTRACTORS
  • PACKING MEASURE
  • FRACTALS
  • CARPETS
  • DECOMPOSITIONS
  • DEFINITIONS
  • SPECTRUM
  • SETS

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