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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Nevanlinna Theory, Normal Families, and Algebraic Differential Equations (Paperback, 1st ed. 2017)
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Nevanlinna Theory, Normal Families, and Algebraic Differential Equations (Paperback, 1st ed. 2017)
Series: Universitext
Expected to ship within 10 - 15 working days
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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 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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