Nevanlinna Theory, Normal Families, and Algebraic Differential Equations / Universitext (PDF)
(Sprache: Englisch)
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...
Following a comprehensive treatment of Nevanlinna's...
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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 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.
Autoren-Porträt von Norbert Steinmetz
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.
Bibliographische Angaben
- Autor: Norbert Steinmetz
- 2017, 1st ed. 2017, 235 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319598007
- ISBN-13: 9783319598000
- Erscheinungsdatum: 24.07.2017
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
eBook Informationen
- Dateiformat: PDF
- Größe: 3.49 MB
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Sprache:
Englisch
Pressezitat
“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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