Skip to content
Register Sign in Wishlist

Automorphisms and Equivalence Relations in Topological Dynamics


Part of London Mathematical Society Lecture Note Series

  • Date Published: June 2014
  • availability: Available
  • format: Paperback
  • isbn: 9781107633223

£ 51.99

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • 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.

    • The authors' original approach provides a clearer and simpler treatment of some key ideas and classical results
    • Provides plenty of scope for further research
    • The self-contained exposition and detailed proofs give a level of rigour that will appeal to both novices and experts
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: June 2014
    • format: Paperback
    • isbn: 9781107633223
    • length: 281 pages
    • dimensions: 229 x 152 x 16 mm
    • weight: 0.42kg
    • contains: 80 exercises
    • availability: Available
  • Table of Contents

    Part I. Universal Constructions:
    1. The Stone–Cech compactification βT
    Appendix to Chapter 1. Ultrafilters and the construction of βT
    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 τ-Topology:
    10. The τ-topology on Aut(X)
    11. The derived group
    12. Quasi-factors and the τ-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.

  • Authors

    David B. Ellis, Beloit College, Wisconsin
    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, University of Minnesota
    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.

Related Books

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.