An introduction to developments in chaos and related topics in nonlinear dynamics, including the detection and quantification of chaos in experimental data, fractals, and complex systems. Most of the important elementary concepts in nonlinear dynamics are discussed, with emphasis on the physical concepts and useful results rather than mathematical proofs and derivations. While many books on chaos are purely qualitative and many others are highly mathematical, this book fills the middle ground by giving the essential equations, but in the simplest possible form. It assumes only an elementary knowledge of calculus. Complex numbers, differential equations, and vector calculus are used in places, but those tools are described as required. The book is aimed at the student, scientist, or engineer who wants to learn how to use the ideas in a practical setting. It is written at a level suitable for advanced undergraduate and beginning graduate students in all fields of science and engineering.
Professor Julien Clinton Sprott Department of Physics University of Wisconsin-Madison 1150 University Avenue Madison Wisconsin 53706 USA Tel: 001-608-263-4449 Email: firstname.lastname@example.org http://sprott.physics.wisc.edu/
Preface ; 1. Introduction ; 2. One-dimensional maps ; 3. Nonchaotic multidimensional flows ; 4. Dynamical systems theory ; 5. Lyapunov exponents ; 6. Strange attractors ; 7. Bifurcations ; 8. Hamiltonian chaos ; 9. Time-series properties ; 10. Nonlinear prediction and noise reduction ; 11. Fractals ; 12. Calculation of fractal dimension ; 13. Fractal measure and multifractals ; 14. Nonchaotic fractal sets ; 15. Spatiotemporal chaos and complexity ; A. Common chaotic systems ; B. Useful mathematical formulas ; C. Journals with chaos and related papers ; Bibliography ; Index