Extremal rate of convergence in discrete hyperbolic and parabolic dynamics

Fuente: arXiv
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Main Authors: Cruz-Zamorano, Francisco J., Zarvalis, Konstantinos
Format: Preprint
Published: 2025
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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
id 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