Multifractal analysis for Bedford-McMullen carpets
Thomas Jordan, Michal Rams
TL;DR
This paper extends the multifractal analysis of Bernoulli measures supported on Bedford-McMullen carpets, removing previous separation assumptions and providing a more general understanding of their local dimension structure.
Contribution
It introduces a multifractal analysis for Bedford-McMullen carpets without requiring strong separation conditions, broadening the applicability of previous results.
Findings
Multifractal spectrum computed for Bedford-McMullen carpets.
Analysis extends previous work by removing separation assumptions.
Provides new insights into local dimensions of Bernoulli measures.
Abstract
In this paper we compute the multifractal analysis for local dimensions of Bernoulli measures supported on the self-affine carpets introduced by Bedford-McMullen. This extends the work of King where the multifractal analysis is computed with strong additional separation assumptions.
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Taxonomy
TopicsMathematical Dynamics and Fractals