Semigroups of holomorphic functions; rectifiability and Lipschitz properties of the orbits
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913963119214592 |
|---|---|
| author | Betsakos, Dimitrios Zarvalis, Konstantinos |
| author_facet | Betsakos, Dimitrios Zarvalis, Konstantinos |
| contents | Let $(ϕ_t)$ be a semigroup of holomorphic functions in the unit disk. We prove that all its orbits are rectifiable and that its forward orbits are Lipschitz curves. Moreover, we find a necessary and sufficient condition in terms of hyperbolic geometry so that a backward orbit is a Lipschitz curve. We further explore the Lipschitz condition for forward orbits lying on the unit circle and then for semigroups of holomorphic functions in general simply connected domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semigroups of holomorphic functions; rectifiability and Lipschitz properties of the orbits Betsakos, Dimitrios Zarvalis, Konstantinos Complex Variables Let $(ϕ_t)$ be a semigroup of holomorphic functions in the unit disk. We prove that all its orbits are rectifiable and that its forward orbits are Lipschitz curves. Moreover, we find a necessary and sufficient condition in terms of hyperbolic geometry so that a backward orbit is a Lipschitz curve. We further explore the Lipschitz condition for forward orbits lying on the unit circle and then for semigroups of holomorphic functions in general simply connected domains. |
| title | Semigroups of holomorphic functions; rectifiability and Lipschitz properties of the orbits |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2501.01952 |