图书简介

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 H閚on 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.

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