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2005•Mathematical Proceedings of the Cambridge Philosophical SocietyRequires access

Metric properties of the Julia set of some meromorphic functions with an asymptotic value eventually mapped onto a pole

Bartłomiej Skorulski

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Abstract

We study the dynamics of non-entire transcendental meromorphic functions with a finite asymptotic value mapped after some iterations onto a pole. This situation does not appear in the case of rational or entire functions. We consider the family of non-entire functions \[ f(z)=\frac{a\exp(z^p)+b\exp(-z^p)}{c\exp(z^p)+d\exp(-z^p)} \] with this property, i.e. there exists a finite asymptotic value .

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What this paper is about

We study the dynamics of non-entire transcendental meromorphic functions with a finite asymptotic value mapped after some iterations onto a pole. This situation does not appear in the case of rational or entire functions. We consider the family of non-entire functions \[ f(z)=\frac{a\exp(z^p)+b\exp(-z^p)}{c\exp(z^p)+d\exp(-z^p)} \] with this property, i.e. there exists a finite asymptotic value .

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Available abstract

We study the dynamics of non-entire transcendental meromorphic functions with a finite asymptotic value mapped after some iterations onto a pole. This situation does not appear in the case of rational or entire functions. We consider the family of non-entire functions \[ f(z)=\frac{a\exp(z^p)+b\exp(-z^p)}{c\exp(z^p)+d\exp(-z^p)} \] with this property, i.e. there exists a finite asymptotic value .

Key concepts: Meromorphic function, Julia set, Mathematics, Entire function, Transcendental number, Value (mathematics), Metric (unit), Transcendental function

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