Polynomials in molecules
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918305872216064 |
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| author | Gao, Yan Zeng, Jinsong |
| author_facet | Gao, Yan Zeng, Jinsong |
| contents | This paper characterizes polynomials within molecules. We show that a geometrically finite polynomial of degree $d\geq2$ lies in a molecule if and only if all its critical points belong to maximal Fatou chains, and show that distinct molecules are mutually disjoint. We also establish a necessary and sufficient condition for subhyperbolic polynomials to be on the closures of bounded hyperbolic components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18605 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomials in molecules Gao, Yan Zeng, Jinsong Dynamical Systems 37F20, 37F10 This paper characterizes polynomials within molecules. We show that a geometrically finite polynomial of degree $d\geq2$ lies in a molecule if and only if all its critical points belong to maximal Fatou chains, and show that distinct molecules are mutually disjoint. We also establish a necessary and sufficient condition for subhyperbolic polynomials to be on the closures of bounded hyperbolic components. |
| title | Polynomials in molecules |
| topic | Dynamical Systems 37F20, 37F10 |
| url | https://arxiv.org/abs/2601.18605 |