Wow! eBook
Automorphisms and Equivalence Relations in Topological Dynamics
Author(s): David B. Ellis (Author), Robert Ellis (Author)
- Publisher: Cambridge University Press
- Publication Date: August 11, 2014
- Edition: 1st
- Language: English
- Print length: 281 pages
- ISBN-10: 1107633222
- ISBN-13: 9781107633223
Book 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.
Editorial Reviews
Book Description
A lucid and self-contained treatment of many key ideas in topological dynamics, achieved by focusing on equivalence relations and automorphisms.
About the Author
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.
