Universitext

Dynamical Systems

An Introduction

Authors: Barreira, Luis, Valls, Claudia

  • Short and self-contained introduction to dynamical systems
  • Direct and rigorous exposition
  • Contains a large number of examples and exercises
  • Includes an accessible introduction to ergodic theory
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Softcover $69.95
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  • ISBN 978-1-4471-4834-0
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About this Textbook

The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction.

Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem.

The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology.

This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.

Reviews

From the reviews:

“The volume is organized into eight chapters, with the first introductory chapter briefly summarizing the contents of the remaining chapters. … the book does cover the topic of dynamical systems thoroughly and from both the discrete dynamics and the continuous dynamics points of view, including topologic and symbolic dynamics and ergodic theory. Summing Up: Recommended. Upper-division undergraduates, graduate students, and researchers/faculty.” (M. D. Sanford, Choice, Vol. 51 (3), November, 2013)

“This book is an introductory text to the modern theory of dynamical systems, with particular focus on discrete time systems. It is written as a text book for undergraduate or beginning graduate courses. The book is almost self contained: it includes all the definitions, with examples, and the proofs of the presented results, as well as the majority of the tools in the proofs. The last section of each chapter consists of a list of exercises.” (Pau Martin de la Torre, zbMATH, Vol. 1269, 2013)

Table of contents (8 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4471-4835-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-1-4471-4834-0
  • 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
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Bibliographic Information

Bibliographic Information
Book Title
Dynamical Systems
Book Subtitle
An Introduction
Authors
Series Title
Universitext
Copyright
2013
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-4471-4835-7
DOI
10.1007/978-1-4471-4835-7
Softcover ISBN
978-1-4471-4834-0
Series ISSN
0172-5939
Edition Number
1
Number of Pages
IX, 209
Number of Illustrations and Tables
44 b/w illustrations
Topics