Generalised dimensions of measures on self-affine sets

Kenneth John Falconer

doi:10.1088/0951-7715/12/4/308

Generalised dimensions of measures on self-affine sets

Kenneth John Falconer

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	877-891
Number of pages	15
Journal	Nonlinearity
Volume	12
Issue number	4
DOIs	https://doi.org/10.1088/0951-7715/12/4/308
Publication status	Published - Jul 1999

Keywords

STRANGE ATTRACTORS
MULTIFRACTAL FORMALISM
HAUSDORFF DIMENSION
SIERPINSKI CARPETS
FRACTALS
SPECTRUM

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10.1088/0951-7715/12/4/308

Cite this

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AB - 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.

KW - STRANGE ATTRACTORS

KW - MULTIFRACTAL FORMALISM

KW - HAUSDORFF DIMENSION

KW - SIERPINSKI CARPETS

KW - FRACTALS

KW - SPECTRUM

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VL - 12

SP - 877

EP - 891

JO - Nonlinearity

JF - Nonlinearity

IS - 4

ER -

Generalised dimensions of measures on self-affine sets

Abstract

Keywords

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