Analytic mappings of the unit disk which almost preserve hyperbolic area
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909321530441728 |
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| author | Ivrii, Oleg Nicolau, Artur |
| author_facet | Ivrii, Oleg Nicolau, Artur |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic mappings of the unit disk which almost preserve hyperbolic area Ivrii, Oleg Nicolau, Artur Complex Variables Classical Analysis and ODEs 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. |
| title | Analytic mappings of the unit disk which almost preserve hyperbolic area |
| topic | Complex Variables Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2403.02798 |