Non-bulging Fatou components for transcendental skew-products
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915894860447744 |
|---|---|
| author | Potthink, Tom Raissy, Jasmin |
| author_facet | Potthink, Tom Raissy, Jasmin |
| contents | In this paper, we investigate the bulging of escaping or oscillating Fatou components on invariant fibers for general skew-products, with a focus on the dependence on the perturbation. We show that any orbitally unbounded component is non-bulging for an appropriate choice of perturbation, whereas sufficiently well-behaved perturbations can render it bulging when the fiber is attracting. Our results highlight that bulging is influenced by more than just the dynamics on the fiber and in the one-dimensional coordinate, contrasting sharply with established results for non-escaping Fatou components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26202 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-bulging Fatou components for transcendental skew-products Potthink, Tom Raissy, Jasmin Dynamical Systems Primary 37F80, Secondary 30D05, 32H50, 37F10 In this paper, we investigate the bulging of escaping or oscillating Fatou components on invariant fibers for general skew-products, with a focus on the dependence on the perturbation. We show that any orbitally unbounded component is non-bulging for an appropriate choice of perturbation, whereas sufficiently well-behaved perturbations can render it bulging when the fiber is attracting. Our results highlight that bulging is influenced by more than just the dynamics on the fiber and in the one-dimensional coordinate, contrasting sharply with established results for non-escaping Fatou components. |
| title | Non-bulging Fatou components for transcendental skew-products |
| topic | Dynamical Systems Primary 37F80, Secondary 30D05, 32H50, 37F10 |
| url | https://arxiv.org/abs/2603.26202 |