Nevanlinna Theory, Normal Families, and Algebraic Differential Equations - Universitext (Paperback)
  • Nevanlinna Theory, Normal Families, and Algebraic Differential Equations - Universitext (Paperback)

Nevanlinna Theory, Normal Families, and Algebraic Differential Equations - Universitext (Paperback)

Paperback 235 Pages / Published: 07/08/2017
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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 Painleve-Yosida theorem, which relates Painleve 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.

Publisher: Springer International Publishing AG
ISBN: 9783319597997
Number of pages: 235
Weight: 3927 g
Dimensions: 235 x 155 mm
Edition: 1st ed. 2017

"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)

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