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Complex Dynamics

  • Textbook
  • © 1993

Overview

Authors:
  1. Lennart Carleson

    1. Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden
      Department of Mathematics, University of California, Los Angeles, USA

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  2. Theodore W. Gamelin

    1. Department of Mathematics, University of California, Los Angeles, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Universitext (UTX)

Part of the book sub series: Universitext: Tracts in Mathematics (3080)

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About this book

Complex dynamics is today very much a focus of interest. Though several fine expository articles were available, by P. Blanchard and by M. Yu. Lyubich in particular, until recently there was no single source where students could find the material with proofs. For anyone in our position, gathering and organizing the material required a great deal of work going through preprints and papers and in some cases even finding a proof. We hope that the results of our efforts will be of help to others who plan to learn about complex dynamics and perhaps even lecture. Meanwhile books in the field a. re beginning to appear. The Stony Brook course notes of J. Milnor were particularly welcome and useful. Still we hope that our special emphasis on the analytic side will satisfy a need. This book is a revised and expanded version of notes based on lectures of the first author at UCLA over several \Vinter Quarters, particularly 1986 and 1990. We owe Chris Bishop a great deal of gratitude for supervising the production of course notes, adding new material, and making computer pictures. We have used his computer pictures, and we will also refer to the attractive color graphics in the popular treatment of H. -O. Peitgen and P. Richter. We have benefited from discussions with a number of colleagues, and from suggestions of students in both our courses.

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Conformal and Quasiconformal Mappings

    • Lennart Carleson, Theodore W. Gamelin
    Pages 1-25

  3. Fixed Points and Conjugations

    • Lennart Carleson, Theodore W. Gamelin
    Pages 27-51

  4. Basic Rational Iteration

    • Lennart Carleson, Theodore W. Gamelin
    Pages 53-67

  5. Classification of Periodic Components

    • Lennart Carleson, Theodore W. Gamelin
    Pages 69-80

  6. Critical Points and Expanding Maps

    • Lennart Carleson, Theodore W. Gamelin
    Pages 81-98

  7. Applications of Quasiconformal Mappings

    • Lennart Carleson, Theodore W. Gamelin
    Pages 99-108

  8. Local Geometry of the Fatou Set

    • Lennart Carleson, Theodore W. Gamelin
    Pages 109-122

  9. Quadratic Polynomials

    • Lennart Carleson, Theodore W. Gamelin
    Pages 123-159

  10. Back Matter

    Pages 161-177
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Authors and Affiliations

  • Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

    Lennart Carleson

  • Department of Mathematics, University of California, Los Angeles, USA

    Lennart Carleson, Theodore W. Gamelin

Bibliographic Information

  • Book Title: Complex Dynamics

  • Authors: Lennart Carleson, Theodore W. Gamelin

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4612-4364-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1993

  • Softcover ISBN: 978-0-387-97942-7Published: 23 July 1993

  • eBook ISBN: 978-1-4612-4364-9Published: 11 November 2013

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: IX, 192

  • Topics: Analysis

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