Exploring Chaos: Theory And Experiment - Couverture rigide

Davies, Brian

Couverture rigide

ISBN 10 : 0738200905 ISBN 13 : 9780738200903

Editeur : Westview Press, 1999

Synopsis

Chaos theory is not just of interest to the physical sciences. Davies (mathematics, Australian National U.) introduces the theory of chaos (including fractals) in non-linear dynamic systems coupled with numerical and graphical representation, without resorting to advanced calculus and algebra. Appendices provide documentation for Chaos for Java software, a discussion of computing various types of equations, and a list of dimensional maps. Annotation c. Book News, Inc., Portland, OR (booknews.com)

A propos du livre

Présentation de l'éditeur

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

Biographie de l'auteur

Brian Davies is a Professor of Mathematics at the Australian National University in Canberra, ACT. His research interests include exactly integrable non-linear quantum systems, lattice statistical mechanics, non-linear dynamical systems and chaos, and the use of computers in teaching. He has been a visiting fellow at Oxford University, Bristol University, and the Free University (Berlin). He has published many articles in his field.

Détails de l'édition

• Éditeur: Westview Press
• Date d'édition: 1999
• Langue: anglais
• ISBN 10: 0738200905
• ISBN 13: 9780738200903
• Reliure: Relié
• Nombre de pages: 237
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible