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arXiv · 2412.14924

Dynamics of complex harmonic mappings

Gopal Datt·Ramanpreet Kaur
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Abstract

This note initiates the study of the Fatou\,--\,Julia sets of a complex harmonic mapping. Along with some fundamental properties of the Fatou and the Julia sets, we observe some contrasting behaviour of these sets as those with in case of a holomorphic function. The existence of harmonic mapping with a wandering domain is also shown.

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Gopal Datt, Ramanpreet Kaur. 2024-12-19. Dynamics of complex harmonic mappings. https://arxiv.org/abs/2412.14924

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