Nevanlinna Theory, Normal Families, and Algebraic Differential Equations
Authors: Steinmetz, Norbert
Free Preview- 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
Buy this book
- 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.
- Reviews
-
“The book by Steinmetz is clearly written, including a substantial number of exercises related to and complementing the actual text.” (Ilpo Laine, Mathematical Reviews, June, 2018)
“The list of references contains more than 200 items including very recent results of the author and other. … I recommend this book to any person who is interested in complex analysis, in particular, in value distribution theory and complex differential equations.” (Igor Chyzhykov, zbMATH, 2018)
- Table of contents (6 chapters)
-
-
Selected Topics in Complex Analysis
Pages 1-31
-
Nevanlinna Theory
Pages 33-73
-
Selected Applications of Nevanlinna Theory
Pages 75-112
-
Normal Families
Pages 113-136
-
Algebraic Differential Equations
Pages 137-172
-
Table of contents (6 chapters)
Buy this book
Services for this Book
Recommended for you
Bibliographic Information
- Bibliographic Information
-
- Book Title
- Nevanlinna Theory, Normal Families, and Algebraic Differential Equations
- Authors
-
- Norbert Steinmetz
- 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
- 8 b/w illustrations
- Topics
