Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules

Michael Baake; Robert V. Moody

Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules

Mathematical Physics 2007-05-23 v1 Combinatorics Metric Geometry math.MP

Authors: Michael Baake , Robert V. Moody

Abstract

The problem of invariance and self-similarity in Z-modules is investigated. For a selection of examples relevant to quasicrystals, especially Fibonacci modules, we determine the semigroup of self-similarities and encapsulate the number of similarity submodules in terms of Dirichlet series generating functions.

Keywords

model sets cut and project sets self-similarities translation group averaging operators invariant densities diffraction

Cite

@article{arxiv.math-ph/9809008,
  title  = {Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules},
  author = {Michael Baake and Robert V. Moody},
  journal= {arXiv preprint arXiv:math-ph/9809008},
  year   = {2007}
}

Comments

7 pages; to appear in: Aperiodic 97, eds. M. de Boissieu, J. L. Verger-Gaugry and R. Currat, World Scientific, Singapore (1998), in press

Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules

Abstract

Keywords

Cite

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