Entire maps with rational preperiodic points and multipliers
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908485632917504 |
|---|---|
| author | Buff, Xavier Gorbovickis, Igors Huguin, Valentin |
| author_facet | Buff, Xavier Gorbovickis, Igors Huguin, Valentin |
| contents | Given a number field $\mathbb{K} \subset \mathbb{C}$ that is not contained in $\mathbb{R}$, we prove the existence of a dense set of entire maps $f \colon \mathbb{C} \rightarrow \mathbb{C}$ whose preperiodic points and multipliers all lie in $\mathbb{K}$. This contrasts with the case of rational maps. In addition, we show that there exists an escaping quadratic-like map that is not conjugate to an affine escaping quadratic-like map and whose multipliers all lie in $\mathbb{Q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13674 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entire maps with rational preperiodic points and multipliers Buff, Xavier Gorbovickis, Igors Huguin, Valentin Dynamical Systems 37F10, 37P35 (Primary) Given a number field $\mathbb{K} \subset \mathbb{C}$ that is not contained in $\mathbb{R}$, we prove the existence of a dense set of entire maps $f \colon \mathbb{C} \rightarrow \mathbb{C}$ whose preperiodic points and multipliers all lie in $\mathbb{K}$. This contrasts with the case of rational maps. In addition, we show that there exists an escaping quadratic-like map that is not conjugate to an affine escaping quadratic-like map and whose multipliers all lie in $\mathbb{Q}$. |
| title | Entire maps with rational preperiodic points and multipliers |
| topic | Dynamical Systems 37F10, 37P35 (Primary) |
| url | https://arxiv.org/abs/2304.13674 |