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2011•Journal of MathematicsRequires access

SOME DYNAMICAL PROPERTIES OF TRANSCENDENTAL ENTIRE FUNCTIONS

Zhigang Huang

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Abstract

In this paper,we study some dynamical properties of Fatou set of random iteration generated by a family of transcendental entire functions {f_1,f_2,…,f_m}.By using the theory of complex dynamics and hyperbolic metric on hyperbolic domain,we obtain a criterion condition for non-existence of the bounded components of Fatou set.This is an answer to the question raised by Baker.We also give out a sufficient condition for which the Fatou components of random iteration system are simply connected,which is an improvement of Bergweiler's result.

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In this paper,we study some dynamical properties of Fatou set of random iteration generated by a family of transcendental entire functions {f_1,f_2,…,f_m}.By using the theory of complex dynamics and hyperbolic metric on hyperbolic domain,we obtain a criterion condition for non-existence of the bounded components of Fatou set.This is an answer to the question raised by Baker.We also give out a sufficient condition for which the Fatou components of random iteration system are simply connected,which is an improvement of Bergweiler's result.

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Available abstract

In this paper,we study some dynamical properties of Fatou set of random iteration generated by a family of transcendental entire functions {f_1,f_2,…,f_m}.By using the theory of complex dynamics and hyperbolic metric on hyperbolic domain,we obtain a criterion condition for non-existence of the bounded components of Fatou set.This is an answer to the question raised by Baker.We also give out a sufficient condition for which the Fatou components of random iteration system are simply connected,which is an improvement of Bergweiler's result.

Key concepts: Mathematics, Julia set, Entire function, Transcendental number, Bounded function, Metric (unit), Pure mathematics, Domain (mathematical analysis)

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