Automorphisms and Equivalence Relations in Topological Dynamics
Published on 5. June 2014
Book
Paperback/Softback
281 pages
978-1-107-63322-3 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 17 mm
Weight
465 gr
ISBN-13
978-1-107-63322-3 (9781107633223)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
David B. Ellis | Robert Ellis
Automorphisms and Equivalence Relations in Topological Dynamics
E-Book
06/2014
1st Edition
Cambridge University Press
€58.99
Available for download
E-Book
06/2014
Cambridge University Press
€49.49
Available for download
Persons
David B. Ellis received his PhD in algebraic topology from the University of California, Berkeley. He has taught at a wide variety of institutions including Yale University, Vassar College, and Washington University in St Louis, and is currently a member of the faculty at Beloit College in Wisconsin. He has published papers in algebraic topology, foliations, fractal geometry and topological dynamics. Robert Ellis, a student of W. Gottschalk, is one of the founders of topological dynamics. He received his PhD from the University of Pennsylvania. During his long and productive career he made many major contributions to the abstract theory of topological dynamics, including his joint continuity theorem and the introduction of the enveloping semigroup. In so doing he laid the foundation for an algebraic approach to topological dynamics. Professor Ellis retired from the University of Minnesota in 1995 and was named a fellow of the AMS in 2012.
Content
Part I. Universal Constructions: 1. The Stone-Cech compactification ?T; Appendix to Chapter 1. Ultrafilters and the construction of ?T; 2. Flows and their enveloping semigroups; 3. Minimal sets and minimal right ideals; 4. Fundamental notions; 5. Quasi-factors and the circle operator; Appendix to Chapter 5. The Vietoris topology on 2^X; Part II. Equivalence Relations and Automorphisms: 6. Quotient spaces and relative products; 7. Icers on M and automorphisms of M; 8. Regular flows; 9. The quasi-relative product; Part III. The ?-Topology: 10. The ?-topology on Aut(X); 11. The derived group; 12. Quasi-factors and the ?-topology; Part IV. Subgroups of G and the Dynamics of Minimal Flows: 13. The proximal relation and the group P; 14. Distal flows and the group D; 15. Equicontinuous flows and the group E; Appendix to Chapter 15. Equicontinuity and the enveloping semigroup; 16. The regionally proximal relation; Part V. Extensions of Minimal Flows: 17. Open and highly proximal extensions; Appendix. Extremely disconnected flows; 18. Distal extensions of minimal flows; 19. Almost periodic extensions; 20. A tale of four theorems.