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arXiv:2301.00662 [math.DS]AbstractReferencesReviewsResources

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

Tao Chen, Yunping Jiang, Linda Keen

Published 2023-01-02Version 1

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.

Comments: 5 figures
Categories: math.DS, math.CV
Subjects: 37F10, 30F05, 30D05, 37A30
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