Developments in Mathematics

Inverse Limits

From Continua to Chaos

Authors: Ingram, W.T., Mahavier, William S.

  • An elementary introduction to inverse limits through inverse limits on [0,1] is included in the first chapter
  • The general theory of inverse limits is presented for compact Hausdorff spaces over directed sets using set valued functions in chapter two
  • Special topics from continuum theory such as indecomposability are discussed in detail An appendix containing mostly an introduction to the topology of the Hilbert cube is included
  • An extensive bibliography listing much of the literature on inverse limits is a part of the book
see more benefits

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-1797-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4614-1796-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4939-0074-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families.

This book will serve as a useful reference to graduate students and researchers in continuum theory and dynamical systems. Researchers working in applied areas who are discovering inverse limits in their work will also benefit from this book.

Reviews

From the reviews:

“Inverse limits are an important tool to study some aspects of the theory of continua. They provide a powerful tool for constructing interesting and complicated examples. This book is an excellent introduction to this topic and it is also useful for researchers since it includes the new developments in this area. The spaces considered here are always continua. … The book finishes with a very complete bibliography that includes 591 items.” (Alejandro Illanes, Zentralblatt MATH, Vol. 1234, 2012)


Table of contents (5 chapters)

  • Inverse Limits on Intervals

    Ingram, W. T. (et al.)

    Pages 1-74

  • Inverse Limits in a General Setting

    Ingram, W. T. (et al.)

    Pages 75-129

  • Inverse Limits in Continuum Theory

    Ingram, W. T. (et al.)

    Pages 131-154

  • Brown’s Approximation Theorem

    Ingram, W. T. (et al.)

    Pages 155-165

  • Appendix: An Introduction to the Hilbert Cube

    Ingram, W. T. (et al.)

    Pages 167-187

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-1797-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4614-1796-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4939-0074-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Inverse Limits
Book Subtitle
From Continua to Chaos
Authors
Series Title
Developments in Mathematics
Series Volume
25
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-1797-2
DOI
10.1007/978-1-4614-1797-2
Hardcover ISBN
978-1-4614-1796-5
Softcover ISBN
978-1-4939-0074-9
Series ISSN
1389-2177
Edition Number
1
Number of Pages
XVI, 220
Topics