Self-Similarities and Invariant Densities for Model Sets
Mathematical Physics
2007-05-23 v1 Condensed Matter
math.MP
Abstract
Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of translations of a lattice. This leads us to the concept of averaging operators and invariant densities on model sets. We prove that invariant densities exist and that they produce absolutely continuous invariant measures in internal space. We study the invariant densities and their relationships to diffraction, continuous refinement operators, and Hutchinson measures.
Cite
@article{arxiv.math-ph/9809006,
title = {Self-Similarities and Invariant Densities for Model Sets},
author = {Michael Baake and Robert V. Moody},
journal= {arXiv preprint arXiv:math-ph/9809006},
year = {2007}
}
Comments
15 pages, 2 figures, to appear in: Algebraic Methods and Theoretical Physics (ed. Y. St. Aubin)