Extremal rate of convergence in continuous 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 deals with semigroups of holomorphic self-maps of the upper half-plane that exhibit an extremal (i.e. the slowest possible) rate of convergence to their Denjoy--Wolff point. The main novelty lies in the parabolic case of zero hyperbolic step. We provide several characterizations for such semigroups in terms of the Herglotz representation of their infinitesimal generators, the conformality at the Denjoy--Wolff point of a modification of their associated Koenigs function, and more.
format Preprint
id arxiv_https___arxiv_org_abs_2510_20953
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Extremal rate of convergence in continuous dynamics
Cruz-Zamorano, Francisco J.
Zarvalis, Konstantinos
Complex Variables
Dynamical Systems
Primary: 37F44, 37F99, Secondary: 30C35, 30E20
This paper deals with semigroups of holomorphic self-maps of the upper half-plane that exhibit an extremal (i.e. the slowest possible) rate of convergence to their Denjoy--Wolff point. The main novelty lies in the parabolic case of zero hyperbolic step. We provide several characterizations for such semigroups in terms of the Herglotz representation of their infinitesimal generators, the conformality at the Denjoy--Wolff point of a modification of their associated Koenigs function, and more.
title Extremal rate of convergence in continuous dynamics
topic Complex Variables
Dynamical Systems
Primary: 37F44, 37F99, Secondary: 30C35, 30E20
url https://arxiv.org/abs/2510.20953