Chaos: The Science of Predictable Random Motion
This is an excellent book. The author systematically introduces the major concepts using simple models (particularly pendulum) and iterations of algebraic equations, visualizations based on these and amplified by interactive media on an accompanying CD. Systems of increasing complexity: 1D, 2D, 3D were pursued. Each step is built on from previous ones and there is useful repetition of previous ideas. This exploration is put into a wonderful historical context . I found these historical vignettes one of the most enjoyable parts of the book and they blended well with the exposition. The evolution of the subject (the motivations, starts and stops) was partitioned naturally within the progressive exposition in the text.
I read this shortly after reading An Introduction To Chaotic Dynamical Systems by Robert L. Devaney. The central concepts of the characteristics of chaos: sensitivity to initial conditions; topological transitivity and dense set of periodic orbits were explored and explained in a clear and deep (yet deceptively simple manner). I developed deeper insights into concepts I found difficult: including homoclinic points,, homoclinic trajectories, heteroclinic trajectories. The use of Liapunov exponent was very helpful.
Finally, the culmination of potential applications and range of disciplines: Conway’s game of life, Wolfram classification of cellular automata, control systems, biomedical science, forecasting was a great way to pull together all the ideas.