Iterated Function Systems and Permutation Representations of the Cuntz Algebra

Introduction Permutative representations of $\mathcal O_N$ Monomial representations and integers modulo $N$ Cycles of irreducible $\mathcal O_N$ representations and their atoms of UHF$_N$ representations Relations of finite type and sub-Cuntz states The shift representation The universal permutative multiplicity-free representation Some specific examples of the cycle and atom structure: The mod $N$ case Some specific examples of the cycle and atom structure: The mod $\mathbf N$ case The general mod $\mathbf N$ situation Concluding remarks Bibliography List of symbols.