3 problems

Let $\mathcal{C}_d$ be the connectedness locus of the space $\mathcal{P}_d$ of degree-$d$ polynomials, and let a polynomial in $\mathcal{C}_d$ be combinatorially rigid if it has no…

Let $f$ be a polynomial with Julia set $J$, and suppose that $J$ is locally connected. Assume that almost every point of $J$ with respect to harmonic (Brolin) measure is the landin…

Landing conjecture for external rays. Every ray $R_M(\theta)$ lands for every $\theta\in\mathbb{R}/\mathbb{Z}$, and $\widehat{\mathcal{R}}$ is exactly the set of angles whose corre…