Journal ArticleDOI
Non-real periodic points of entire functions
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In this article, it was shown that if f is an entire transcendental function, l a straight line in the complex plane, and n ≥ 2, then f has infinitely many repelling periodic points of period n that do not lie on l.Abstract:
Abstract It is shown that if f is an entire transcendental function, l a straight line in the complex plane, and n ≥ 2, then f has infinitely many repelling periodic points of period n that do not lie on l.read more
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Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of finite order
Volker Mayer,Mariusz Urbański +1 more
TL;DR: In this paper, the authors use Nevanlinna theory to provide full thermodynamical formalism for a very general class of meromorphic functions of finite order and provide the multifractal analysis of Gibbs states.
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Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of Finite Order
Volker Mayer,Mariusz Urbański +1 more
TL;DR: In this paper, the authors provide a systematic account of the thermodynamical formalism for such a meromorphic function f and all potentials that are Holder perturbations of -t log /f'/omega.
Journal ArticleDOI
On an application of Lambert's W function to infinite exponentials
TL;DR: In this paper, the authors survey the basic results concerning the convergence of infinite exponential functions and derive exact expansions for finite and infinite power iterates of the hyperpower function for real and complex cases.
On the derivatives of composite functions
Eleanor Lingham,James K. Langley +1 more
TL;DR: In this paper, it was shown that for a non-constant polynomial and a rational function, the function (f √ √ g) √ (k) has infinitely many zeros.
Book ChapterDOI
Singular Values of Meromorphic Functions
TL;DR: In this paper, the singular value of a meromorphic function is defined as any neighborhood of which the inverse of the function contains a multiple-valued branch, and a value is a singular value if and only if it is an asymptotic value or a critical value.
References
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On Meromorphic Functions. I
TL;DR: In this article, the applications of homogeneous differential polynomials to the Nevanlinna theory of meromorphic functions in the finite complex plane have been given, and some generalizations by these polynomial coefficients have been shown.
Journal ArticleDOI
Eindeutige analytische Funktionen: R. Nevanlinna (Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Bd. 46), VIII+353 S. J. Springer, Berlin 1936. Preis geb. RM 29,40
Journal ArticleDOI
Periodic points of entire functions: proof of a conjecture of Baker
TL;DR: In this article, it was shown that if n ≥ 2, then there are infinitely many fixpoints of an entire transcendental function which are not fixpoints for any k satisfying 1 ≤ k ≤ n.