One-dimensional dynamics has generated many results, and avenues of active mathematical research with numerous inroads to this research remain to be pursued by the advanced undergraduate or beginning graduate student. While much of the material in this book is not covered elsewhere, some aspects present new research topics whose connections are drawn to other research areas from the text. Although the material presented is not meant to be approached in a linear fashion, anybody with an interest in dynamics will find many topics of interest.

1. Topological roots 2. Measure theoretic roots 3. Symbolic and topological dynamics 4. Beginning measurable dynamics 5. 2 Map 6. Kneading maps 7. Some number theory 8. Circle maps 9. Topological entropy 10. Symmetric tent maps 11. Adding machines and maps 12. Beta-transformations and maps 13. Homeomorphic restrictions 14. Complex quadratic dynamics.

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