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arXiv · 2403.02798

Analytic mappings of the unit disk which almost preserve hyperbolic area

Oleg Ivrii·Artur Nicolau
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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, Möbius distortion, the distribution of critical points and Aleksandrov-Clark measures. We also study Lyapunov exponents of their Aleksandrov-Clark measures.

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Oleg Ivrii, Artur Nicolau. 2024-09-20. Analytic mappings of the unit disk which almost preserve hyperbolic area. https://arxiv.org/abs/2403.02798

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