Dynamical Systems and Chaos

ISBN-13: 9781461427124 / Angielski / Miękka / 2012 / 313 str.

Henk Broer; Floris Takens

Opis

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.

Recenzje

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 Kovacic, 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)

Spis treści

Examples and definitions of dynamical phenomena.- Qualitative properties and predictability of evolutions.- Persistence of dynamical properties.- Global structure of dynamical systems.- On KAM Theory.- Reconstruction and time series analysis.

O autorze

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

Blurb

Over the last four decades there has been extensive development in the theory of dynamical systems. This book starts from the phenomenological point of view reviewing examples. Hence the authors discuss oscillators, like the pendulum in many variation including damping and periodic forcing , the Van der Pol System, the Henon and Logistic families, the Newton algorithm seen as a dynamical system and the Lorenz and Rossler system are also discussed. The phenomena concern equilibrium, periodic, multi- or quasi-periodic and chaotic dynamic dynamics as these occur in all kinds of modeling and are met both in computer simulations and in experiments. The application areas vary from celestial mechanics and economical evolutions to population dynamics and climate variability. The book is aimed at a broad audience of students and researchers. The first four chapters have been used for an undergraduate course in Dynamical Systems and material from the last two chapters and from the appendices has been used for master and PhD courses by the authors. All chapters conclude with an exercise section. 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. Henk Broer and Floris Takens, professors at the Institute for Mathematics and Computer Science of the University of Groningen, are leaders in the field of dynamical systems. They have published a wealth of scientific papers and books in this area and both authors are members of the Royal Netherlands Academy of Arts and Sciences (KNAW).