Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

Norbert steinmetz (author)

235 pages, parution le 06/08/2017

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Résumé

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.

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 a

t 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.1st Edition 2017th editionIllustrationsQA331Nevanlinna theory.|Differential equations.|Algebra.1SwitzerlandCham9783319598000|9783319598017Norbert Steinmetz.Universitext

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Norbert steinmetz (author)
Parution	06/08/2017
Nb. de pages	235
Format	155 x 235
Poids	397g
EAN13	9783319597997

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Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

Résumé

Caractéristiques techniques

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