Extremal rate of convergence in continuous dynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914111160320000 |
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| author | Cruz-Zamorano, Francisco J. Zarvalis, Konstantinos |
| author_facet | Cruz-Zamorano, Francisco J. Zarvalis, Konstantinos |
| contents | This paper deals with semigroups of holomorphic self-maps of the upper half-plane that exhibit an extremal (i.e. the slowest possible) rate of convergence to their Denjoy--Wolff point. The main novelty lies in the parabolic case of zero hyperbolic step. We provide several characterizations for such semigroups in terms of the Herglotz representation of their infinitesimal generators, the conformality at the Denjoy--Wolff point of a modification of their associated Koenigs function, and more. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremal rate of convergence in continuous dynamics Cruz-Zamorano, Francisco J. Zarvalis, Konstantinos Complex Variables Dynamical Systems Primary: 37F44, 37F99, Secondary: 30C35, 30E20 This paper deals with semigroups of holomorphic self-maps of the upper half-plane that exhibit an extremal (i.e. the slowest possible) rate of convergence to their Denjoy--Wolff point. The main novelty lies in the parabolic case of zero hyperbolic step. We provide several characterizations for such semigroups in terms of the Herglotz representation of their infinitesimal generators, the conformality at the Denjoy--Wolff point of a modification of their associated Koenigs function, and more. |
| title | Extremal rate of convergence in continuous dynamics |
| topic | Complex Variables Dynamical Systems Primary: 37F44, 37F99, Secondary: 30C35, 30E20 |
| url | https://arxiv.org/abs/2510.20953 |