Nevanlinna Theory, Normal Families, and Al...

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Beschreibung

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 Nevanlinnäs 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.

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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2017
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xviii 235 S. 8 s/w Illustr. 235 p. 8 illus.
ISBN-13:	9783319597997
ISBN-10:	331959799X
Sprache:	Englisch
Herstellernummer:	978-3-319-59799-7
Einband:	Kartoniert / Broschiert
Autor:	Steinmetz, Norbert
Auflage:	1st edition 2017
Hersteller:	Springer International Publishing Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 15 mm
Von/Mit:	Norbert Steinmetz
Erscheinungsdatum:	07.08.2017
Gewicht:	0,394 kg

Artikel-ID: 109588719