Local connectivity of Julia sets of some transcendental entire functions with Siegel disks
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866908353760854016 |
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| author | Yang, Fei Zhang, Gaofei Zhang, Yanhua |
| author_facet | Yang, Fei Zhang, Gaofei Zhang, Yanhua |
| contents | Based on the weak expansion property of a long iteration of a family of quasi-Blaschke products near the unit circle established recently, we prove that the Julia sets of a number of transcendental entire functions with bounded type Siegel disks are locally connected. In particular, if $θ$ is of bounded type, then the Julia set of the sine function $S_θ(z)=e^{2πiθ}\sin(z)$ is locally connected. Moreover, we prove the existence of transcendental entire functions having Siegel disks and locally connected Julia sets with asymptotic values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local connectivity of Julia sets of some transcendental entire functions with Siegel disks Yang, Fei Zhang, Gaofei Zhang, Yanhua Dynamical Systems Complex Variables Based on the weak expansion property of a long iteration of a family of quasi-Blaschke products near the unit circle established recently, we prove that the Julia sets of a number of transcendental entire functions with bounded type Siegel disks are locally connected. In particular, if $θ$ is of bounded type, then the Julia set of the sine function $S_θ(z)=e^{2πiθ}\sin(z)$ is locally connected. Moreover, we prove the existence of transcendental entire functions having Siegel disks and locally connected Julia sets with asymptotic values. |
| title | Local connectivity of Julia sets of some transcendental entire functions with Siegel disks |
| topic | Dynamical Systems Complex Variables |
| url | https://arxiv.org/abs/2505.04944 |