Authors:
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Developments in Mathematics (DEVM, volume 25)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
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)
Authors and Affiliations
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Science and Technology, Mathematics and Statistics, Missouri University of, Rolla, USA
W.T. Ingram
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, Professor Emeritus, Emory University, Atlanta, USA
William S. Mahavier
Bibliographic Information
Book Title: Inverse Limits
Book Subtitle: From Continua to Chaos
Authors: W.T. Ingram, William S. Mahavier
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-1-4614-1797-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Hardcover ISBN: 978-1-4614-1796-5Published: 05 November 2011
Softcover ISBN: 978-1-4939-0074-9Published: 25 January 2014
eBook ISBN: 978-1-4614-1797-2Published: 06 November 2011
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XVI, 220