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Conformal Fractals
Ergodic Theory Methods

$94.99 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: June 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521438001

$ 94.99 (C)
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About the Authors
  • This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research.

    • A self-contained introduction suitable for graduate students, including exercises
    • Brings together a wide variety of methods and results previously scattered throughout the literature
    • Provides pointers to further reading and links to related areas of research
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    Reviews & endorsements

    "This book provides a broad and self-contained introduction to the theory of uniformly and non-uniformly expanding holomorphic maps. This book is a valuable resource for fundamental results and a comprehensive state of the art reference for recent developments in the field."
    Katrin Gelfert, Mathematical Reviews

    "Conformal Fractals is packed with classical gems with proofs provided. The authors are experts on extending the subject in many of the important directions it has taken the past several decades, especially the move from uniformly hyperbolic maps to expansive maps, which includes many rational maps of the sphere. This is an interesting text that could be used for a year-long graduate course in ergodic theory..."
    Jane Hawkins, Bulletin of the American Mathematical Society

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    Product details

    • Date Published: June 2010
    • format: Paperback
    • isbn: 9780521438001
    • length: 366 pages
    • dimensions: 228 x 152 x 18 mm
    • weight: 0.52kg
    • contains: 26 b/w illus. 90 exercises
    • availability: Available
  • Table of Contents

    Introduction
    Basic examples and definitions
    1. Measure preserving endomorphisms
    2. Compact metric spaces
    3. Distance expanding maps
    4. Thermodynamical formalism
    5. Expanding repellers in manifolds and in the Riemann sphere, preliminaries
    6. Cantor repellers in the line, Sullivan's scaling function, application in Feigenbaum universality
    7. Fractal dimensions
    8. Conformal expanding repellers
    9. Sullivan's classification of conformal expanding repellers
    10. Holomorphic maps with invariant probability measures of positive Lyapunov exponent
    11. Conformal measures
    References
    Index.

  • Authors

    Feliks Przytycki, Polish Academy of Sciences
    Feliks Przytycki is a Professor in the Institute of Mathematics at the Polish Academy of Sciences.

    Mariusz Urbański, University of North Texas
    Mariusz Urbanski is a Professor in the Department of Mathematics at the University of North Texas.

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