TY - JOUR
T1 - Analytic mappings of the unit disk which almost preserve hyperbolic area
AU - Ivrii, Oleg
AU - Nicolau, Artur
N1 - Publisher Copyright:
© 2024 The Authors. Proceedings of the London Mathematical Society is copyright © London Mathematical Society.
PY - 2024/10/30
Y1 - 2024/10/30
N2 - In this paper, we study analytic self-maps of the unit disk which distort hyperbolic areas 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 examine the Lyapunov exponents of their Aleksandrov–Clark measures.
AB - In this paper, we study analytic self-maps of the unit disk which distort hyperbolic areas 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 examine the Lyapunov exponents of their Aleksandrov–Clark measures.
KW - Sets
UR - https://www.scopus.com/pages/publications/85208133606
UR - https://www.mendeley.com/catalogue/01739698-60a3-38db-9656-f9954d2a38ed/
U2 - 10.1112/plms.70001
DO - 10.1112/plms.70001
M3 - Article
AN - SCOPUS:85208133606
SN - 0024-6115
VL - 129
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
IS - 5
M1 - e70001
ER -