Steinmetz N. Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

Springer International Publishing AG, 2017. — 249 p. — (Universitext) — ISBN: 978-3-319-59799-7.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.Selected Topics in Complex Analysis
Nevanlinna Theory
Selected Applications of Nevanlinna Theory
Normal Families
Algebraic Differential Equations
Higher-Order Algebraic Differential Equations