Examples in Discrete Iteration of Arbitrary Intervals of Slopes
Given a compact interval [a, b]⊂[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 D...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/169508 |
| Online Access: | https://hdl.handle.net/11441/169508 https://doi.org/10.1007/s12220-025-01934-4 |
| Access Level: | Open access |
| Keyword: | Complex dynamics Discrete iteration The slope problem |
| Summary: | Given a compact interval [a, b]⊂[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. |
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