Monotonicity properties of hyperbolic projections in holomorphic iteration
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912447043993600 |
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| author | Christodoulou, Argyrios Zarvalis, Konstantinos |
| author_facet | Christodoulou, Argyrios Zarvalis, Konstantinos |
| contents | We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, necessary, assumptions, the projections exhibit monotonicity properties akin to those present in continuous dynamics. Our techniques are purely hyperbolic-geometric in nature and provide the general framework for analysing projections of arbitrary sequences onto curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotonicity properties of hyperbolic projections in holomorphic iteration Christodoulou, Argyrios Zarvalis, Konstantinos Complex Variables Primary: 37F44, 30F45, Secondary: 30D05, 51M10 We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, necessary, assumptions, the projections exhibit monotonicity properties akin to those present in continuous dynamics. Our techniques are purely hyperbolic-geometric in nature and provide the general framework for analysing projections of arbitrary sequences onto curves. |
| title | Monotonicity properties of hyperbolic projections in holomorphic iteration |
| topic | Complex Variables Primary: 37F44, 30F45, Secondary: 30D05, 51M10 |
| url | https://arxiv.org/abs/2506.19562 |