Topics from One-Dimensional Dynamics

One-dimensional dynamics owns many deep results and avenues of active mathematical research. Numerous inroads to this research exist for the advanced undergraduate or beginning graduate student. This book provides glimpses into one-dimensional dynamics with the hope that the results presented illuminate the beauty and excitement of the field. Much of this material is covered nowhere else in textbook format, some are mini new research topics in themselves, and novel connections are drawn with other research areas both inside and outside the text. The material presented here is not meant to be approached in a linear fashion. Readers are encouraged to pick and choose favourite topics. Anyone with an interest in dynamics, novice or expert alike, will find much of interest within.

Spis treści:
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.