On a complex-analytic approach to stationary measures on $S^1$ with respect to the action of $PSU(1,1)$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912331841142784 |
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| author | Kosenko, Petr |
| author_facet | Kosenko, Petr |
| contents | We provide a complex-analytic approach to the classification of stationary probability measures on $S^1$ with respect to the action of $PSU(1,1)$ on the unit circle via Möbius transformations by studying their Cauchy transforms from the perspective of generalized analytic continuation. We improve upon results of Bourgain and present a complete characterization of Furstenberg measures for Fuchsian groups of first kind via the Brown-Shields-Zeller theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11065 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a complex-analytic approach to stationary measures on $S^1$ with respect to the action of $PSU(1,1)$ Kosenko, Petr Dynamical Systems Functional Analysis Probability 05C81, 42B30 We provide a complex-analytic approach to the classification of stationary probability measures on $S^1$ with respect to the action of $PSU(1,1)$ on the unit circle via Möbius transformations by studying their Cauchy transforms from the perspective of generalized analytic continuation. We improve upon results of Bourgain and present a complete characterization of Furstenberg measures for Fuchsian groups of first kind via the Brown-Shields-Zeller theorem. |
| title | On a complex-analytic approach to stationary measures on $S^1$ with respect to the action of $PSU(1,1)$ |
| topic | Dynamical Systems Functional Analysis Probability 05C81, 42B30 |
| url | https://arxiv.org/abs/2403.11065 |