Minimal Flows and Their Extensions - 1st Edition - ISBN: 9780444704535, 9780080872643

Minimal Flows and Their Extensions, Volume 153

1st Edition

Authors: J. Auslander
eBook ISBN: 9780080872643
Imprint: North Holland
Published Date: 1st July 1988
Page Count: 264
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Table of Contents

Flows and Minimal Sets. Equicontinuous Flows. The Enveloping Semigroup of a Transformation Group, I. Joint Continuity Theorems. Distal Flows. The Enveloping Semigroup, II. The Furstenberg Structure Theorem for Distal Minimal Flows. Universal Minimal Flows and Ambits. The Equicontinuous Structure Relation and Weakly Mixing Flows. The Algebraic Theory of Minimal Flows. Disjointness. Invariant Measures on Flows. Kakutani-Bebutov Theorems. General Structure Theorems. Appendices: Nets. Uniform Spaces.


Description

This monograph presents developments in the abstract theory of topological dynamics, concentrating on the internal structure of minimal flows (actions of groups on compact Hausdorff spaces for which every orbit is dense) and their homomorphisms (continuous equivariant maps).

Various classes of minimal flows (equicontinuous, distal, point distal) are intensively studied, and a general structure theorem is obtained. Another theme is the universal'' approach - entire classes of minimal flows are studied, rather than flows in isolation. This leads to the consideration of disjointness of flows, which is a kind of independence condition. Among the topics unique to this book are a proof of the Ellisjoint continuity theorem'', a characterization of the equicontinuous structure relation, and the aforementioned structure theorem for minimal flows.


Details

No. of pages:
264
Language:
English
Copyright:
© North Holland 1988
Published:
Imprint:
North Holland
eBook ISBN:
9780080872643

Reviews

@qu:The leisurely pace, clarity of presentation and the self consistency which is carefully preserved throughout makes it ideal for graduate students seeking an introduction to this branch of topological dynamics. @source:E. Glasner Bulletin of the American Mathematical Society @from:R. Ellis @qu:The book under review is a pleasant, leisurely account of the topics discussed. In places it reads like a novel. The author's approach to the subject might be termed `topological' as opposed to `algebraic'; he stresses the former and down-plays the latter wherever possible. @source:Ergodic Theory & Dynamical Systems


About the Authors

J. Auslander Author