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arXiv · 2411.11975

Examples in Discrete Iteration of Arbitrary Intervals of Slopes

Manuel D. Contreras·Francisco J. Cruz-Zamorano·Luis Rodríguez-Piazza
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Abstract

Given a compact interval $[a,b] \subset [0,\pi]$, 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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Manuel D. Contreras, Francisco J. Cruz-Zamorano, Luis Rodríguez-Piazza. 2024-11-18. Examples in Discrete Iteration of Arbitrary Intervals of Slopes. https://arxiv.org/abs/2411.11975

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