Examples in Discrete Iteration of Arbitrary Intervals of Slopes

Fuente: arXiv
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Auteurs principaux: Contreras, Manuel D., Cruz-Zamorano, Francisco J., Rodríguez-Piazza, Luis
Format: Preprint
Publié: 2024
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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