Extremal rate of convergence in continuous dynamics
Complex Variables
2025-10-27 v1 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.2510.20953,
title = {Extremal rate of convergence in continuous dynamics},
author = {Francisco J. Cruz-Zamorano and Konstantinos Zarvalis},
journal= {arXiv preprint arXiv:2510.20953},
year = {2025}
}
Comments
29 pages