Eventually dendric subshifts

TL;DR

This paper introduces eventually dendric subshifts, a new class of shift spaces that includes Sturmian shifts, and demonstrates their closure properties under conjugacy and complete bifix decoding.

Contribution

The paper defines eventually dendric subshifts and proves their closure under conjugacy and complete bifix decoding transformations.

Findings

Includes Sturmian shifts in the class

Proves closure under conjugacy

Proves closure under complete bifix decoding

Abstract

We define a new class of shift spaces which contains a number of classes of interest, like Sturmian shifts used in discrete geometry. We show that this class is closed under two natural transformations. The first one is called conjugacy and is obtained by sliding block coding. The second one is called the complete bifix decoding, and typically includes codings by non overlapping blocks of fixed length.