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＜電子ブック＞
Nevanlinna Theory, Normal Families, and Algebraic Differential Equations / by Norbert Steinmetz
(Universitext. ISSN:21916675)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
本文言語	英語
大きさ	XVIII, 235 p. 8 illus : online resource
著者標目	*Steinmetz, Norbert author SpringerLink (Online service)
件　名	LCSH:Functions of complex variables LCSH:Differential equations LCSH:Difference equations LCSH:Functional equations FREE:Functions of a Complex Variable FREE:Differential Equations FREE:Difference and Functional Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-59800-0

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