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arXiv · 2604.12240

Brennan Conjecture for Basin of Attraction at Infinity

Yigang Zheng
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Abstract

This paper investigates the Brennan Conjecture for domains $\Omega$ 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.

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Yigang Zheng. 2026-04-14. Brennan Conjecture for Basin of Attraction at Infinity. https://arxiv.org/abs/2604.12240

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