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Book synopsis

This 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, Poincare sections, and return maps. Please visit http://www.maths.anu.edu.au/~briand/chaos/ for the integrated cross-platform software.

Book details

Book category Books in English Mathematics & science Mathematics

• Full title: Exploring Chaos
• Subtitle: Theory And Experiment
• Author: Brian Davies
• Language: English
• Binding: Paperback
• Number of pages: 256
• EAN: 9780813341279
• ISBN: 0813341272
• ID: 04725187
• Publisher: Taylor & Francis Inc
• Weight: 398 g
• Dimensions: 152 × 229 × 22 mm
• Date of publishing: 10. October 2003

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