Dynamics of complex harmonic mappings
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910851467837440 |
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| author | Datt, Gopal Kaur, Ramanpreet |
| author_facet | Datt, Gopal Kaur, Ramanpreet |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of complex harmonic mappings Datt, Gopal Kaur, Ramanpreet Complex Variables Dynamical Systems 30D05, 30D45, 37F10 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. |
| title | Dynamics of complex harmonic mappings |
| topic | Complex Variables Dynamical Systems 30D05, 30D45, 37F10 |
| url | https://arxiv.org/abs/2412.14924 |