 |
 |
|
|
 |
 |
 Exploring ChaosTheory And Experimentby Brian Davies Oct 9, 2003
DescriptionThis book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. The theory is developed using only elementary calculus and algebra, and includes dynamics of one-and two-dimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and bifurcation theory of one-dimensional systems. There is an introduction to the theory of fractals, with an emphasis on the importance of scaling, and a concluding chapter on ordinary differential equations. The accompanying software, written in Java, is available online (see link below). The program enables students to carry out their own quantitative experiments on a variety of nonlinear systems, including the analysis of fixed points of compositions of maps, calculation of Fourier spectra and Lyapunov exponents, and box counting for two-dimensional maps. It also provides for visualizing orbits, final state and bifurcation diagrams, Fourier spectra and Lyapunov exponents, basins of attractions, three-dimensional orbits, Poincaré sections, and return maps. Please visit http://www.maths.anu.edu.au/~briand/chaos/ for the integrated cross-platform software. Reviews”This book is a clearly written and concise text that avoids lengthy explanations and excessive mathematical detail, making it accessible for intermediate undergraduate students in either mathematics or nearly any of the sciences. An instructor searching for a text with such features would do well to check out both this book and its accompanying software.” ”The book will be useful to undergraduate science and mathematics students who would like to understand the proofs behind our understanding of the dynamics of discrete-time nonlinear systems. The text also provides a nice collection of computer exercises based on the author’s software.” ”This is one of the best entries in the recent crop of moderately sized, mathematically oriented, introductions to Chaos Theory. The author has cleverly chosen subjects whose rigorous treatments lie just within range of elementary calculus and algebra. The narrative flows with deceptive ease, the definitions are carefully crafted, the mathematical derivations are short enough not to interrupt the train of the exposition.” ”(A) unique addition to the long list of books on chaos in dynamical systems. It fills a niche in the market by providing both an excellent introductory text and a fully integrated suite of readily available software at the undergraduate level. The book is a very fine example of contemporary teaching practice, through which the author has done a great service to the mathematics community.” ”The great strength of this book and the accompanying software is the simplicity of presentation which succinctly guides the user through potentially complex topics such as universal scaling exponents, fractals, numerical shadowing, ergodicity, feedback control and Lyapunov exponents.” ”Brian Davies has written an excellent book for students and their teachers. The book truly is about exploring chaos, hands-on. The software is nicely designed, easy to use, and well integrated with the text. Davies is a fine teacher. He takes care to motivate some of the more difficult and subtle aspects of nonlinear dynamics.” ”This is a book which ought to be in every physics library (and, of course, in every math library). Anyone wanting to obtain a deeper understanding of chaos, or presenting a course on it, ought to think about buying the book. It is suitable for an undergraduate course in computational mathematics or theoretical physics.” Selling TerritoryWorld |
|
 |
