Analytic mappings of the unit disk which almost preserve hyperbolic area
Complex Variables
2024-09-24 v2 Classical Analysis and ODEs
Abstract
In this paper, we study analytic self-maps of the unit disk which distort hyperbolic area of large hyperbolic disks by a bounded amount. We give a number of characterizations involving angular derivatives, Lipschitz extensions, M\"obius distortion, the distribution of critical points and Aleksandrov-Clark measures. We also study Lyapunov exponents of their Aleksandrov-Clark measures.
Keywords
Cite
@article{arxiv.2403.02798,
title = {Analytic mappings of the unit disk which almost preserve hyperbolic area},
author = {Oleg Ivrii and Artur Nicolau},
journal= {arXiv preprint arXiv:2403.02798},
year = {2024}
}
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44 pages