Elementary properties of circle map sequences

TL;DR

This paper investigates the combinatorial and structural characteristics of circle map sequences, introducing an embedding procedure to analyze the hull and classifying admissible words based on their occurrence.

Contribution

It presents a novel embedding method to study the hull structure and classifies admissible words in circle map sequences.

Findings

Developed an embedding procedure for hull analysis

Classified admissible words by their appearance

Enhanced understanding of sequence structure

Abstract

We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we study the structure of the hull. We also study the set of admissible words and classify them in terms of their appearance.