Self-Similar Measures for Quasicrystals

Details Self-Similar Measures for Quasicrystals Self-Similar Measures for Quasicrystals

2000-08-08

arxiv.org/abs/math/0008063v1

Directions in Mathematical Quasicrystals (eds. M. Baake and R.V. Moody), CRM Monograph Series, vol. 13, AMS, Providence, RI (2

Mathematics

Metric Geometry

42 pages, several figures

Scientific paper

We study self-similar measures of Hutchinson type, defined by compact
families of contractions, both in a single and multi-component setting. The
results are applied in the context of general model sets to infer, via a
generalized version of Weyl's Theorem on uniform distribution, the existence of
invariant measures for families of self-similarities of regular model sets.

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