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Nevanlinna theory, normal families, ...

Steinmetz, Norbert.

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Nevanlinna theory, normal families, and algebraic differential equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Nevanlinna theory, normal families, and algebraic differential equations/ by Norbert Steinmetz.
作者:	Steinmetz, Norbert.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xviii, 235 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Nevanlinna theory. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-59800-0
ISBN:	9783319598000

Nevanlinna theory, normal families, and algebraic differential equations
Steinmetz, Norbert.

Nevanlinna theory, normal families, and algebraic differential equations[electronic resource] /by Norbert Steinmetz. - Cham :Springer International Publishing :2017. - xviii, 235 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

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 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.

ISBN: 9783319598000

Standard No.: 10.1007/978-3-319-59800-0doiSubjects--Topical Terms:

711035
Nevanlinna theory.

LC Class. No.: QA331

Dewey Class. No.: 515.9

Nevanlinna theory, normal families, and algebraic differential equations
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520 $a 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.
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