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Universitext

Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

Authors: Steinmetz, Norbert

  • Provides a self-contained introduction to Nevanlinna theory and normal families
  • Collects recent results on first-order and Painlevé differential equations, and 2D Hamiltonian systems
  • Presents applications of Nevanlinna theory to the value distribution of differential polynomials and uniqueness of meromorphic functions
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eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-59800-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-59799-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

Norbert Steinmetz graduated from and held his first academic positions at Technische Universität (TU) Karlsruhe (now KIT). Later he held the chair Funktionentheorie (Complex Analysis) at TU Dortmund for almost 25 years. His research interests include Nevanlinna theory, ordinary differential equations in the complex domain, and complex dynamics. He has written a number of research articles and a book on rational iteration.

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Table of contents (6 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-59800-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-59799-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nevanlinna Theory, Normal Families, and Algebraic Differential Equations
Authors
Series Title
Universitext
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-59800-0
DOI
10.1007/978-3-319-59800-0
Softcover ISBN
978-3-319-59799-7
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XVIII, 235
Number of Illustrations and Tables
8 b/w illustrations
Topics