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  • © 2003

Combinations of Complex Dynamical Systems

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1827)

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  • ISBN: 978-3-540-39936-0
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Table of contents (11 chapters)

  1. Front Matter

    Pages I-IX
  2. 1 Introduction

    • Kevin M. Pilgrim
    Pages 1-35
  3. 2 Preliminaries

    • Kevin M. Pilgrim
    Pages 37-48
  4. 3 Combinations

    • Kevin M. Pilgrim
    Pages 49-57
  5. 4 Uniqueness of combinations

    • Kevin M. Pilgrim
    Pages 59-68
  6. 5 Decomposition

    • Kevin M. Pilgrim
    Pages 69-77
  7. 6 Uniqueness of decompositions

    • Kevin M. Pilgrim
    Pages 79-81
  8. 7 Counting classes of annulus maps

    • Kevin M. Pilgrim
    Pages 83-88
  9. 8 Applications to mapping class groups

    • Kevin M. Pilgrim
    Pages 89-94
  10. 9 Examples

    • Kevin M. Pilgrim
    Pages 95-103
  11. 10 Canonical Decomposition Theorem

    • Kevin M. Pilgrim
    Pages 105-109
  12. References

    • Kevin M. Pilgrim
    Pages 111-116
  13. Back Matter

    Pages 117-118

About this book

This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere. It is intended for researchers interested in the classification of those complex one-dimensional dynamical systems which are in some loose sense tame. The program is motivated by the dictionary between the theories of iterated rational maps and Kleinian groups.

Keywords

  • Canon
  • Complex dynamics
  • Counting
  • boundary element method
  • class
  • classification
  • dynamical systems
  • mapping
  • object
  • postcritically finite
  • theorem

Bibliographic Information

Buying options

eBook USD 34.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-39936-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 49.95
Price excludes VAT (USA)