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 oneand twodimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and bifurcation theory of onedimensional 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 twodimensional maps. It also provides for visualizing orbits, final state and bifurcation diagrams, Fourier spectra and Lyapunov exponents, basins of attractions, threedimensional orbits, Poincaré sections, and return maps. Please visit http://www.maths.anu.edu.au/~briand/chaos/ for the integrated crossplatform software.


About the Author


Brian Davies is a Professor of Mathematics at the Australian National University in Canberra, ACT. His research interests include exactly integrable nonlinear quantum systems, lattice statistical mechanics, nonlinear 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.

