On the Combinatorial Rigidity for Polynomials with Attracting Cycles
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914379510841344 |
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| author | Wang, Yueyang |
| author_facet | Wang, Yueyang |
| contents | We show that every polynomial of degree $d \geq 2$ in the connectedness locus with an attracting cycle which attracts at least two critical points and no indifferent cycles is not combinatorially rigid. In particular, we prove that a hyperbolic polynomial with connected Julia set is combinatorially rigid if and only if it is of the ``disjoint type''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06277 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Combinatorial Rigidity for Polynomials with Attracting Cycles Wang, Yueyang Dynamical Systems Complex Variables We show that every polynomial of degree $d \geq 2$ in the connectedness locus with an attracting cycle which attracts at least two critical points and no indifferent cycles is not combinatorially rigid. In particular, we prove that a hyperbolic polynomial with connected Julia set is combinatorially rigid if and only if it is of the ``disjoint type''. |
| title | On the Combinatorial Rigidity for Polynomials with Attracting Cycles |
| topic | Dynamical Systems Complex Variables |
| url | https://arxiv.org/abs/2603.06277 |