Dynamical Systems and Chaos

1. Front Matter

   Pages i-xvi

   PDF

2. Examples and definitions of dynamical phenomena

   • Henk Broer, Floris Takens

   Pages 1-66

3. Qualitative properties and predictability of evolutions

   • Henk Broer, Floris Takens

   Pages 67-108

4. Persistence of dynamical properties

   • Henk Broer, Floris Takens

   Pages 109-132

5. Global structure of dynamical systems

   • Henk Broer, Floris Takens, Floris Takens

   Pages 133-171

6. On KAM theory

   • Henk Broer, Floris Takens

   Pages 173-204

7. Reconstruction and time series analysis

   • Henk Broer, Floris Takens

   Pages 205-242

8. Back Matter

   Pages 243-313

   PDF

Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.

• Bifurcation theory
• Chaotic Dynamics
• Dynamical Systems
• Time series analysis
• periodic and quasi-periodic orbits

From the reviews:

“Today numerous books dealing with either dynamical systems and/or chaos but this one stands out in many ways. Its scope, depth and breath give it a feeling of a must read. … The exercises per chapter run from simple and straightforward to extended research questions forming time-consuming open challenges for the interested reader. All in all a great text written in a very good style for which the authors deserve to be complemented.” (Henk Nijmeijer, Nieuw Archief voor Wiskunde, Vol. 14 (4), December, 2013)

“This work … takes a different tack compared to others. … geared for upper-level undergraduate and graduate students interested in this area of mathematics … . Anyone interested in the field of dynamical systems might like to have this book because of its organization and the ease of finding the often-used examples. Summing Up: Recommended. Upper-division undergraduates through professionals.” (M. D. Sanford, Choice, Vol. 48 (9), May, 2011)

“This book gives a clear and accessible exposition of some of the central concepts addressed by the classical theory of dynamical systems. … The book is very good at bringing out the essence of each concept without unnecessary technical clutter. … this is an excellent book, conveying deep understanding of the subject. It should definitely find its way onto the shelves of the experts, but I also very much recommend it as an excellent supplementary text to a differential equations or dynamical systems course.”­­­ (Gregor Kovačič, SIAM Review, Vol. 53 (4), 2011)

“This is a skillfully written guide to the fundamentals of the theory of dynamical systems and chaos aimed at a wide audience. … the book appeals to a wide audience. It can be successfully used by students, researchers and readers with a good background in differential equations, analysis and topology looking for a concise but informative modern reference on dynamical systems and chaos.” (Svitlana P. Rogovchenko, Zentralblatt MATH, Vol. 1218, 2011)

• Dept. Mathematics, University of Groningen, Groningen, Netherlands

  Henk Broer

• Mathematisch Instituut, Rijksuniversiteit Groningen, Bedum, Netherlands

  Floris Takens

Henk Broer and Floris Takens are professors at the Johann Bernoulli Institute in the University of Groningen.

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