Brennan Conjecture for Basin of Attraction at Infinity

TL;DR

This paper proves the Brennan Conjecture for basins of attraction of certain polynomials, extending previous results to a broader class with small non-leading coefficients.

Contribution

It extends the Brennan Conjecture verification to monic polynomials with small non-leading coefficients for their basins of attraction.

Findings

Brennan Conjecture holds for these basins under specified conditions.

The result generalizes prior work by Baranski, Volberg, and Zdunik.

Applicable to monic polynomials of degree m with small non-leading coefficients.

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.