Bratteli diagrams: structure, measures, dynamics

TL;DR

This survey explores the structure, invariant measures, and dynamics of Bratteli diagrams, including tail measures, continuous dynamics, subdiagrams, and orbit equivalence, providing a comprehensive overview of their mathematical properties.

Contribution

It offers a comprehensive overview of the structure, measures, and dynamics of Bratteli diagrams, highlighting recent developments and open problems in the field.

Findings

Classification of tail invariant measures on Bratteli diagrams

Existence of continuous dynamics compatible with tail equivalence

Analysis of orbit equivalence and full groups

Abstract

This paper is a survey on general (simple and non-simple) Bratteli diagrams which focuses on the following topics: finite and infinite tail invariant measures on the path space $X_B$ of a Bratteli diagram $B$, existence of continuous dynamics on $X_B$ compatible with tail equivalence relation, subdiagrams and measure supports. We also discuss the structure of Bratteli diagrams, orbit equivalence and full groups, homeomorphic measures.