Examples in Discrete Iteration of Arbitrary Intervals of Slopes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912123949416448 |
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| author | Contreras, Manuel D. Cruz-Zamorano, Francisco J. Rodríguez-Piazza, Luis |
| author_facet | Contreras, Manuel D. Cruz-Zamorano, Francisco J. Rodríguez-Piazza, Luis |
| contents | Given a compact interval $[a,b] \subset [0,π]$, we construct a parabolic self-map of the upper half-plane whose set of slopes is $[a,b]$. The nature of this construction is completely discrete and explicit: we explicitly construct a self-map and we explicitly show in which way its orbits wander towards the Denjoy-Wolff point. We also analyze some properties of the Herglotz measure corresponding to such example, which yield the regularity of such self-map in its Denjoy-Wolff point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Examples in Discrete Iteration of Arbitrary Intervals of Slopes Contreras, Manuel D. Cruz-Zamorano, Francisco J. Rodríguez-Piazza, Luis Complex Variables Dynamical Systems Primary 30D05, 37FXX Given a compact interval $[a,b] \subset [0,π]$, we construct a parabolic self-map of the upper half-plane whose set of slopes is $[a,b]$. The nature of this construction is completely discrete and explicit: we explicitly construct a self-map and we explicitly show in which way its orbits wander towards the Denjoy-Wolff point. We also analyze some properties of the Herglotz measure corresponding to such example, which yield the regularity of such self-map in its Denjoy-Wolff point. |
| title | Examples in Discrete Iteration of Arbitrary Intervals of Slopes |
| topic | Complex Variables Dynamical Systems Primary 30D05, 37FXX |
| url | https://arxiv.org/abs/2411.11975 |