Topics from One-Dimensional Dynamics

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Juni 2004



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


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.


Karen M. Brucks is an associate professor at the University of Wisconsin Milwaukee. She has been the recipient of a Fulbright Research Scholar Fellowship and has served on the American Fellowship Panel of the American Association of University Women. Her research interests include topological, measure theoretic, and combinatoric dynamics. Henk Bruin is Lecturer in Mathematics at the University of Surrey. He has also held teaching positions in Germany, Sweden, the Netherlands and the USA, including the position of Taussky-Todd instructor at CalTech. His specialty is one-dimensional chaotic dynamical systems and he has published extensively on most aspects of this theory. His other research interests include counting topology, ergodic theory and complex dynamics.


'... particularly useful for students/beginners in the field. Due to an extensive bibliography, it will also serve as a very good reference book.' European Mathematical Society Newsletter '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
EAN: 9780521547666
ISBN: 0521547660
Untertitel: 'London Mathematical Society St'. Sprache: Englisch.
Erscheinungsdatum: Juni 2004
Seitenanzahl: 297 Seiten
Format: kartoniert
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