Polynomial-like dynamics of analytic maps
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917017889538048 |
|---|---|
| author | Levin, Genadi |
| author_facet | Levin, Genadi |
| contents | The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under some natural conditions, a map of this class has a completely invariant compact set if and only if this set is the filled Julia set of a polynomial-like restriction of the map. We also generalize this result to include maps with non-connected domains of definition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial-like dynamics of analytic maps Levin, Genadi Dynamical Systems Complex Variables The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under some natural conditions, a map of this class has a completely invariant compact set if and only if this set is the filled Julia set of a polynomial-like restriction of the map. We also generalize this result to include maps with non-connected domains of definition. |
| title | Polynomial-like dynamics of analytic maps |
| topic | Dynamical Systems Complex Variables |
| url | https://arxiv.org/abs/2508.17308 |