Dynamics of inner functions revisited
Dynamical Systems
2025-11-20 v4 Complex Variables
Probability
Abstract
We study the circle restrictions of inner functions of the unit disc showing that the local invertibility of a restriction is independent of its singularity set and proving a local characterization of analytic conditional expectations. We establish central limit properties for some stochastic processes driven by probability preserving restrictions via spectral analysis of their perturbed transfer operators.
Keywords
Cite
@article{arxiv.2305.15278,
title = {Dynamics of inner functions revisited},
author = {Jon Aaronson and Mahendra Nadkarni},
journal= {arXiv preprint arXiv:2305.15278},
year = {2025}
}
Comments
34 pages. Some results upgraded and some typos corrected