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Analytic mappings of the unit disk which almost preserve hyperbolic area (2403.02798v2)
Published 5 Mar 2024 in math.CV and math.CA
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.