Brennan Conjecture for Basin of Attraction at Infinity
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908961943322624 |
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| author | Zheng, Yigang |
| author_facet | Zheng, Yigang |
| contents | This paper investigates the Brennan Conjecture for domains $Ω$ that arise as basins of attraction of a polynomial. We extend the result of Baranski, Volberg, and Zdunik to a broader class of polynomials. We prove that for any monic polynomial of degree $m$ with sufficiently small non-leading coefficients, Brennan Conjecture holds for its basin of attraction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12240 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Brennan Conjecture for Basin of Attraction at Infinity Zheng, Yigang Dynamical Systems 30C10, 30C15, 30C35, 30C45, 30C55, 30D30, 37F10 This paper investigates the Brennan Conjecture for domains $Ω$ that arise as basins of attraction of a polynomial. We extend the result of Baranski, Volberg, and Zdunik to a broader class of polynomials. We prove that for any monic polynomial of degree $m$ with sufficiently small non-leading coefficients, Brennan Conjecture holds for its basin of attraction. |
| title | Brennan Conjecture for Basin of Attraction at Infinity |
| topic | Dynamical Systems 30C10, 30C15, 30C35, 30C45, 30C55, 30D30, 37F10 |
| url | https://arxiv.org/abs/2604.12240 |