• Dimension estimate for a set o...

Treffer: Dimension estimate for a set obtained from a three-dimensional non-periodic self-affine tiling

Title:
Dimension estimate for a set obtained from a three-dimensional non-periodic self-affine tiling
Authors:
Sadahiro, Taizo
Publisher Information:
International Society for Mathematical Sciences, Osaka
Subject Terms:
Fractals, PV-numbers and generalizations, other special algebraic numbers, Mahler measure, Pisot number, Relations of ergodic theory with number theory and harmonic analysis, Hausdorff dimension, self-affine tiling, Radix representation, digital problems
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Access URL:
https://zbmath.org/1688870
Accession Number:
edsair.c2b0b933574d..0f9b60f3629811ff6fae91f91c0eb199
Database:
OpenAIRE

Weitere Informationen

For a three-dimensional self-affine tiling generated by the Pisot number satisfying \(x^4=x^3+x^2+x+1\), the Mauldin-Williams graph is used to give explicit bounds for the Hausdorff dimension of an associated subset of the complex plane. Numerical evidence suggests the upper bound obtained is the exact value.