Extremal rate of convergence in discrete hyperbolic and parabolic dynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918160308895744 |
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| author | Cruz-Zamorano, Francisco J. Zarvalis, Konstantinos |
| author_facet | Cruz-Zamorano, Francisco J. Zarvalis, Konstantinos |
| contents | This paper investigates the dynamical behaviour of holomorphic self-maps of the upper half-plane. More precisely, we focus on the hyperbolic and parabolic self-maps whose orbits approach the Denjoy--Wolff point with the slowest possible rate. We characterize self-maps of such extremal rate using various tools, like the Herglotz representation, the conformality of the Koenigs function at the Denjoy--Wolff point and the hyperbolic distance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremal rate of convergence in discrete hyperbolic and parabolic dynamics Cruz-Zamorano, Francisco J. Zarvalis, Konstantinos Complex Variables Dynamical Systems Primary: 30D05, 37F44, 37F99, Secondary: 30C35, 30E20 This paper investigates the dynamical behaviour of holomorphic self-maps of the upper half-plane. More precisely, we focus on the hyperbolic and parabolic self-maps whose orbits approach the Denjoy--Wolff point with the slowest possible rate. We characterize self-maps of such extremal rate using various tools, like the Herglotz representation, the conformality of the Koenigs function at the Denjoy--Wolff point and the hyperbolic distance. |
| title | Extremal rate of convergence in discrete hyperbolic and parabolic dynamics |
| topic | Complex Variables Dynamical Systems Primary: 30D05, 37F44, 37F99, Secondary: 30C35, 30E20 |
| url | https://arxiv.org/abs/2510.12501 |