Nevanlinna theory, normal families, and algebraic differential equations / Norbert Steinmetz.
2017
QA331
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Details
Title
Nevanlinna theory, normal families, and algebraic differential equations / Norbert Steinmetz.
ISBN
9783319598000 (electronic book)
3319598007 (electronic book)
9783319597997
331959799X
3319598007 (electronic book)
9783319597997
331959799X
Published
Cham, Switzerland : Springer, 2017.
Language
English
Description
1 online resource (xviii, 235 pages) : illustrations.
Item Number
10.1007/978-3-319-59800-0 doi
Call Number
QA331
Dewey Decimal Classification
515/.9
Summary
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.-- Provided by publisher.
Note
Includes index.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed August 4, 2017).
Series
Universitext.
Available in Other Form
Print version: 331959799X
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Table of Contents
Introduction and preface
Selected Topics in Complex Analysis
Nevanlinna Theory
Selected Applications of Nevanlinna Theory
Normal Families
Algebraic Differential Equations
Higher-Order Algebraic Differential Equations
Index.
Selected Topics in Complex Analysis
Nevanlinna Theory
Selected Applications of Nevanlinna Theory
Normal Families
Algebraic Differential Equations
Higher-Order Algebraic Differential Equations
Index.