Chaotic Dynamics

Geoffrey R. Goodson is Professor of Mathematics at Towson University, Maryland. He previously served on the faculty of the University of Witwatersrand and the University of Cape Town. His research interests include dynamical systems, ergodic theory, matrix theory, and operator theory. He has published more than thirty papers, and taught numerous classes on dynamical systems.

'This remarkable book provides a thoroughly field-tested way of teaching analysis while introducing dynamical systems. Combining lightness with rigor, it motivates and applies a wide range of subjects in the theory of metric spaces as it explores a broad variety of topics in dynamics.' Boris Hasselblatt, Tufts University, Massachusetts

• 1. The orbits of one-dimensional maps; 2. Bifurcations and the logistic family; 3. Sharkovsky's theorem; 4. Dynamics on metric spaces; 5. Countability, sets of measure zero, and the Cantor set; 6. Devaney's definition of chaos; 7. Conjugacy of dynamical systems; 8. Singer's theorem; 9. Conjugacy, fundamental domains, and the tent family; 10. Fractals; 11. Newton's method for real quadratics and cubics; 12. Coppel's theorem and a proof of Sharkovsky's theorem; 13. Real linear transformations, the Hénon Map, and hyperbolic toral automorphisms; 14. Elementary complex dynamics; 15. Examples of substitutions; 16. Fractals arising from substitutions; 17. Compactness in metric spaces and an introduction to topological dynamics; 18. Substitution dynamical systems; 19. Sturmian sequences and irrational rotations; 20. The multiple recurrence theorem of Furstenberg and Weiss; Appendix A: theorems from calculus; Appendix B: the Baire category theorem; Appendix C: the complex numbers; Appendix D: Weyl's equidistribution theorem.