On weak Wolff--Denjoy theorem for certain non-convex domains
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_ | 1866911576737447936 |
|---|---|
| author | Chandel, Vikramjeet Singh Chatterjee, Sanjoy Sur, Chandan |
| author_facet | Chandel, Vikramjeet Singh Chatterjee, Sanjoy Sur, Chandan |
| contents | In this paper, we provide a class of domains in $\mathbb{C}^3$, such that every holomorphic self-map of that domain either has a fixed point or the sequence of iterates is compactly divergent. In particular, it follows that the symmetrized bidisc, symmetrized tridisc, tetrablock, pentablock are in the aforementioned class of domains. We also give a description of the fixed point set of a holomorphic self-map of the symmetrized bidisc and tetrablock. For the symmetrized bidisc, given a holomorphic self-map such that the sequence of iterates is compactly divergent, we also provide a description of its target set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07215 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On weak Wolff--Denjoy theorem for certain non-convex domains Chandel, Vikramjeet Singh Chatterjee, Sanjoy Sur, Chandan Complex Variables 32H50, 37F99 In this paper, we provide a class of domains in $\mathbb{C}^3$, such that every holomorphic self-map of that domain either has a fixed point or the sequence of iterates is compactly divergent. In particular, it follows that the symmetrized bidisc, symmetrized tridisc, tetrablock, pentablock are in the aforementioned class of domains. We also give a description of the fixed point set of a holomorphic self-map of the symmetrized bidisc and tetrablock. For the symmetrized bidisc, given a holomorphic self-map such that the sequence of iterates is compactly divergent, we also provide a description of its target set. |
| title | On weak Wolff--Denjoy theorem for certain non-convex domains |
| topic | Complex Variables 32H50, 37F99 |
| url | https://arxiv.org/abs/2604.07215 |