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Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

  • Norbert Steinmetz

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Norbert Steinmetz
    Pages 1-31
  3. Norbert Steinmetz
    Pages 33-73
  4. Norbert Steinmetz
    Pages 75-112
  5. Norbert Steinmetz
    Pages 113-136
  6. Norbert Steinmetz
    Pages 137-172
  7. Norbert Steinmetz
    Pages 173-224
  8. Back Matter
    Pages 225-235

About this book

Introduction

This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations.

Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions.

Aimed at graduate students interested
in recent developments in the field and researchers working on related problems,Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.

Keywords

Nevanlinna theory applications of Nevanlinna theory uniqueness theorem complex analysis Yosida Class Zalcman rescaling method Zalcman lemma algebraic functions normal families ordinary differential equations algebraic differential equations asymptotic expansion Yosida rescaling Painlevé transcendents Painlevé property Malmquist theorem Bloch's principle MSC (2010): 30D35, 30D45, 34M05, 34M55, 30D05, 34E05, 34M40

Authors and affiliations

  • Norbert Steinmetz
    • 1
  1. 1.Fakultät für MathematikTU DortmundDortmundGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-59800-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-59799-7
  • Online ISBN 978-3-319-59800-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site