Extremal rate of convergence in discrete hyperbolic and parabolic dynamics

2025/10/14 by Cruz-Zamorano, Francisco J., Zarvalis, Konstantinos · 1 citation
#30E20 #37F44 #37F99 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 30D05 #Secondary: 30C35

paper · doi:10.48550/arxiv.2510.12501

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.

Citations

• Extremal rate of convergence in continuous dynamics
• Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators
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• On Valiron's Theorem

Cited by

• From discrete iteration in the unit disc to continuous semigroups of holomorphic functions

Related

• Extremal rate of convergence in continuous dynamics
• Examples in Discrete Iteration of Arbitrary Intervals of Slopes
• Speeds of Convergence for Petals of Semigroups of Holomorphic Functions
• Rates of convergence for holomorphic semigroups of finite shift
• On the rates of convergence of orbits in semigroups of holomorphic functions