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Topics from One-Dimensional Dynamics

Topics from One-Dimensional Dynamics

£49.99

Part of London Mathematical Society Student Texts

  • Date Published: September 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521547666

£ 49.99
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About the Authors
  • 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.

    • Wide range of topics; many topics covered appear nowhere else in 'text book format'; material is a filering from the research literature of currently active topics
    • Readers encouraged to pick and choose topics of interest, rather than rigid linear fashion
    • Employs style that allows students an active role
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    Reviews & endorsements

    '… 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

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    Product details

    • Date Published: September 2004
    • format: Paperback
    • isbn: 9780521547666
    • length: 312 pages
    • dimensions: 229 x 152 x 19 mm
    • weight: 0.425kg
    • availability: Available
  • Table of Contents

    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.

  • Authors

    Karen M. Brucks, University of Wisconsin, Milwaukee
    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, University of Surrey
    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.

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