Group Colorings and Bernoulli Subflows

ISBN-13: 9781470418472 / Angielski

Su Gao;Steve Jackson;Brandon Seward

Opis

In this paper the authors study the dynamics of Bernoulli flows and their subflows over general countable groups. One of the main themes of this paper is to establish the correspondence between the topological and the symbolic perspectives. From the topological perspective, the authors are particularly interested in free subflows (subflows in which every point has trivial stabilizer), minimal subflows, disjointness of subflows, and the problem of classifying subflows up to topological conjugacy. Their main tool to study free subflows will be the notion of hyper aperiodic points; a point is hyper aperiodic if the closure of its orbit is a free subflow.

Spis treści

• Introduction
• Preliminaries
• Basic constructions of $2$-colorings
• Marker structures and tilings
• Blueprints and fundamental functions
• Basic applications of the fundamental method
• Further study of fundamental functions}
• The descriptive complexity of sets of $2$-colorings
• The complexity of the topological conjugacy relation
• Extending partial functions to $2$-colorings
• Further questions
• Bibliography
• Index