Automorphisms and Equivalence Relations in Topological Dynamics

David B. Ellis, Robert Ellis

• Publisher: Cambridge University Press
• Year: 2014
• Print ISBN: 9781107633223
• eBook ISBN: 9781139950800
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

Focusing on the role that automorphisms and equivalence relations play in the algebraic theory of minimal sets provides an original treatment of some key aspects of abstract topological dynamics. Such an approach is presented in this lucid and self-contained book, leading to simpler proofs of classical results, as well as providing motivation for further study. Minimal flows on compact Hausdorff spaces are studied as icers on the universal minimal flow M. The group of the icer representing a minimal flow is defined as a subgroup of the automorphism group G of M, and icers are constructed explicitly as relative products using subgroups of G. Many classical results are then obtained by examining the structure of the icers on M, including a proof of the Furstenberg structure theorem for distal extensions. This book is designed as both a guide for graduate students, and a source of interesting new ideas for researchers.

Table of contents

• Cover
• Series Page
• Title Page
• Copyright
• Dedication
• Contents
• Introduction
• Part I Universal constructions
• Part II Equivalence relations and automorphisms of flows
• Part III The tau-topology
• Part IV Subgroups of G and the dynamics of minimal flows
• Part V Extensions of minimal flows
• References
• Index