Topics from One-Dimensional Dynamics

An introduction to one-dimensional dynamics for graduate students with novel connections to other areas of mathematics.

Karen M. Brucks (Author), Henk Bruin (Author)

9780521547666, Cambridge University Press

Paperback, published 28 June 2004

312 pages
22.9 x 15.2 x 1.9 cm, 0.425 kg

'This book is intended as a text for an advanced undergraduate or beginning graduate students. As well as providing a brief account on the fundamental concepts of analysis and dynamical systems (Chapters 1-4 and 7-8), and a thorough explanation of topological entropy for piece-wise monotone interval maps (Chapter 9, sometimes with original proofs), the book contains substantial parts on unimodal interval maps and one chapter on complex quadratic polynomials. The quality of this exposition is very good: the material is organized so that all proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples and exercises.' Zentralblatt MATH

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.

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.

Subject Areas: Nonlinear science [PBWR], Applied mathematics [PBW]