Hyperbolic components of cosine family with a fixed critical point
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910049136279552 |
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| author | Qiu, Weiyuan Wang, Lingrui |
| author_facet | Qiu, Weiyuan Wang, Lingrui |
| contents | We studied the parameter plane of the cosine functions with a fixed critical point. The hyperbolic components can be classified into three types: A, C and D. All the hyperbolic components are bounded and simply connected, except for the unique type-A component, which contains 0 as an isolated boundary point. Using the method of para-puzzle, we constructed a phase-parameter transfer mapping and proved that the boundaries of hyperbolic components are Jordan curves. By a similar idea, the hyperbolic components of type C are quasidisks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10554 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hyperbolic components of cosine family with a fixed critical point Qiu, Weiyuan Wang, Lingrui Complex Variables 37F10, 37F15, 30D05 We studied the parameter plane of the cosine functions with a fixed critical point. The hyperbolic components can be classified into three types: A, C and D. All the hyperbolic components are bounded and simply connected, except for the unique type-A component, which contains 0 as an isolated boundary point. Using the method of para-puzzle, we constructed a phase-parameter transfer mapping and proved that the boundaries of hyperbolic components are Jordan curves. By a similar idea, the hyperbolic components of type C are quasidisks. |
| title | Hyperbolic components of cosine family with a fixed critical point |
| topic | Complex Variables 37F10, 37F15, 30D05 |
| url | https://arxiv.org/abs/2603.10554 |