Chaotic Dynamics

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.