Concepts and Results in Chaotic Dynamics: A Short Course

ISBN-13: 9783540347057 / Angielski / Twarda / 2006 / 248 str.

Pierre Collet; Jean Pierre Eckmann

Opis

The study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.

Recenzje

From the reviews:

"The book is a good introduction to the field of dynamical systems with a particular emphasis on statistical properties and applications. In particular, the relations both with real experiments with numerical simulations are discussed. ... The book contains many figures that really help the understanding of the text. The book can be used as a text for an introductory course in dynamical systems (at the master's or Ph.D. level). It is particularly suited for students with interests in applications (either physics, economy or biology)." (Carlangelo Liverani, Mathematical Reviews, Issue 2007 m)

"Two thoughts crossed my mind when I picked up this book. The first was: 'what a physically attractive book.' The second was: 'what a short book to have on such a wide ranging topic.' ... It is a perfect size to carry in a knapsack, the print is clear and the layout of text, equations, and figures is marvelously done. ... images are multi-colored stereo images, and allow the reader to 'see' a three dimensional effect that helps illustrate the phenomena." (David S. Mazel, MathDL, December, 2007)

Spis treści

A Basic Problem.- Dynamical Systems.- Topological Properties.- Hyperbolicity.- Invariant Measures.- Entropy.- Statistics and Statistical Mechanics.- Other Probabilistic Results.- Experimental Aspects.

Blurb

The study of dynamical systems is a well established field. The authors have written this book in an attempt to provide a panorama of several aspects, that are of interest to mathematicians and physicists alike. The book collects the material of several courses at the graduate level given by the authors. Thus, the exposition avoids detailed proofs in exchange for numerous illustrations and examples, while still maintaining sufficient precision. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.