Titlebook: Nevanlinna Theory, Normal Families, and Algebraic Differential Equations; Norbert Steinmetz Textbook 2017 Springer International Publishin

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0172-5939 tial equations, and 2D Hamiltonian systems.Presents applicatThis 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 Ne

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Selected Applications of Nevanlinna Theory,xford, 1964), Laine?(Nevanlinna theory and complex differential equations. De Gruyter studies in mathematics, vol 15. De Gruyter, Boston, 1993), and Wittich?(Neuere Untersuchungen über eindeutige Analytische Funktionen. Springer, Berlin, 1968), nevertheless we will present the basic results in the first section.

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Textbook 2017ic 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 link

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Algebraic Differential Equations,-free regions, asymptotic expansions on pole-free regions, and solutions deviating from the ‘generic’ case. This program will be pursued in the subsequent sections on linear, Riccati, and implicit first-order differential equations.

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Higher-Order Algebraic Differential Equations,d asymptotic expansions on pole-free regions, and characterising the so-called sub-normal solutions. As in the preceding chapter, a crucial role is played by the method of Yosida Re-scaling. It establishes the central discovery that the first, second, and fourth Painlevé transcendents belong to the Yosida classes ., ., ., respectively.

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