Results on Dynamics of Bungee set of Composite Entire Functions in the Eremenko-Lyubich Class
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912780834045952 |
|---|---|
| author | Kumar, Dinesh Das, Soumyajeet |
| author_facet | Kumar, Dinesh Das, Soumyajeet |
| contents | In this paper, we have discussed the dynamics of composite entire functions in terms of relationship between bungee set, escaping set and filled-in Julia set. We have established some relation between the dynamics of composition of entire functions and the functions taken for composition. We have shown that the union of the bungee set of two entire functions contains the bungee set of the composite function. In addition, it is shown that the filled-in Julia set of composite entire functions contains the filled-in Julia set of functions used for the composition. The results have been illustrated with several examples. We have mostly dealt with permutable(commuting) functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11217 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Results on Dynamics of Bungee set of Composite Entire Functions in the Eremenko-Lyubich Class Kumar, Dinesh Das, Soumyajeet Dynamical Systems 37F10, 30D05 In this paper, we have discussed the dynamics of composite entire functions in terms of relationship between bungee set, escaping set and filled-in Julia set. We have established some relation between the dynamics of composition of entire functions and the functions taken for composition. We have shown that the union of the bungee set of two entire functions contains the bungee set of the composite function. In addition, it is shown that the filled-in Julia set of composite entire functions contains the filled-in Julia set of functions used for the composition. The results have been illustrated with several examples. We have mostly dealt with permutable(commuting) functions. |
| title | Results on Dynamics of Bungee set of Composite Entire Functions in the Eremenko-Lyubich Class |
| topic | Dynamical Systems 37F10, 30D05 |
| url | https://arxiv.org/abs/2405.11217 |