Invariant Submodules and Semigroups of Self-Similarities for Fibonacci   Modules
  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. 
Michael Baake, Robert V. Moody