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Problem Books in Mathematics

Dynamical Systems by Example

Authors: Barreira, Luís, Valls, Claudia

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  • Excellent companion to a dynamical systems textbook
  • Includes large variety of problems and accompanying solutions
  • Problems range from simple to complex
  • Emphasis on dynamical systems with discrete time
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eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-030-15915-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
  • ISBN 978-3-030-15914-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Aimed at the graduate/upper undergraduate level, the emphasis is on dynamical systems with discrete time. In addition to the basic theory, the topics include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as basic ergodic theory. As in other areas of mathematics, one can gain the first working knowledge of a topic by solving selected problems. It is rare to find large collections of problems in an advanced field of study much less to discover accompanying detailed solutions. This text fills a gap and can be used as a strong companion to an analogous dynamical systems textbook such as the authors’ own Dynamical Systems (Universitext, Springer) or another text designed for a one- or two-semester advanced undergraduate/graduate course. The book is also intended for independent study.

Problems often begin with specific cases and then move on to general results, following a natural path of learning. They are also well-graded in terms of increasing the challenge to the reader. Anyone who works through the theory and problems in Part I will have acquired the background and techniques needed to do advanced studies in this area. Part II includes complete solutions to every problem given in Part I with each conveniently restated. Beyond basic prerequisites from linear algebra, differential and integral calculus, and complex analysis and topology, in each chapter the authors recall the notions and results (without proofs) that are necessary to treat the challenges set for that chapter, thus making the text self-contained.

 

About the authors

​Luís Barreira is professor of mathematics at the University of Lisbon. His main research interests are in dynamical systems and ergodic theory. Prof. Barreira has authored several books published with Springer including Lyapunov Exponents, Thermodynamic Formalism and Applications to Dimension Theory (PM), (with C. Valls) Dynamical Systems (UTX) and Stability of Nonautonomous Differential Equations (LNM), (with C.  Valls and D. Dragicevic) Admissibility and Hyperbolicity (SBM).
Claudia Valls is professor of mathematics at the University of Lisbon. Her main research interest is in dynamical systems. Prof. Valls has authored several books published with Springer including (with L. Barreira) Dynamical Systems (UTX) and Stability of Nonautonomous Differential Equations (LNM), and (with L. Barreira and D. Dragicevic) Admissibility and Hyperbolicity (SBM).

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Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-030-15915-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
  • ISBN 978-3-030-15914-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Dynamical Systems by Example
Authors
Series Title
Problem Books in Mathematics
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-15915-3
DOI
10.1007/978-3-030-15915-3
Hardcover ISBN
978-3-030-15914-6
Series ISSN
0941-3502
Edition Number
1
Number of Pages
IX, 223
Number of Illustrations
51 b/w illustrations
Topics