On the convergence of boundary points for hyperbolic inner functions

2025/11/25 by Jové, Anna, Mencía, Mateo
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.20502

Abstract

Given a hyperbolic inner function f \colon \mathbbD → \mathbbD with Denjoy-Wolff point p ∈ ∂ \mathbbD, it is well known that almost every point ξ∈ ∂ \mathbbD converges to p under iteration of the radial extension f^* \colon ∂ \mathbbD → ∂ \mathbbD. We provide explicit bounds for the rate of this convergence in terms of the angular derivative, holding almost surely. Our results also cover the case where the Denjoy-Wolff point is a singularity.

Citations

• Shrinking targets and recurrent behaviour for forward compositions of inner functions

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