Substitutional dynamical systems, Bratteli diagrams and dimension groups

TL;DR

This paper introduces an effective, algorithmic method to compute a new invariant for substitution minimal systems using stationary Bratteli diagrams and dimension groups, independent of previously studied spectral invariants.

Contribution

It develops an explicit, algorithmic approach to derive a new invariant for substitution minimal systems based on stationary Bratteli diagrams and dimension groups.

Findings

New invariant is independent of spectral invariants

Method is explicit and algorithmic

Applicable to substitution minimal systems

Abstract

The present paper explores substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithmic and explicit, and render an effective method to compute an invariant of (ordered) $K$-theoretic nature for these systems. This new invariant is independent of spectral invariants which have previously been extensively studied. Before we state the main results we give some background.