Elementary properties of circle map sequences

Abstract

We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map $\Phi: \Omega \to W:= \{ R, L \}^{\bf N}$ from the hull(closure of the set of translates) to the sequence of embedding operations through which we study the structure of $\Omega$. We also study the set of admissible words and classify them in terms of their appearance.