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arXiv · 2510.12501

Extremal rate of convergence in discrete hyperbolic and parabolic dynamics

Francisco J. Cruz-Zamorano·Konstantinos Zarvalis
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Abstract

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.

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Francisco J. Cruz-Zamorano, Konstantinos Zarvalis. 2025-10-14. Extremal rate of convergence in discrete hyperbolic and parabolic dynamics. https://arxiv.org/abs/2510.12501

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