Meromorphic functions whose action on their Julia sets is non-ergodic

Tao Chen; Yunping Jiang; Linda Keen

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arXiv · 2301.00662

Meromorphic functions whose action on their Julia sets is non-ergodic

Tao Chen·Yunping Jiang·Linda Keen

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Abstract

We study transcendental meromorphic functions having two prepole asymptotic values and no critical values. We prove that these functions acting on their Julia sets are non-ergodic, which illustrates the antithesis of the Keen-Kotus result in [KK2] on the ergodicity of another subfamily of functions with two asymptotic values and no critical values.

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Tao Chen, Yunping Jiang, Linda Keen. 2023-01-02. Meromorphic functions whose action on their Julia sets is non-ergodic. https://arxiv.org/abs/2301.00662

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