Mathematics Problem Archive

(Fatou's conjecture) Show that the subset $U$ of functions $g$ in $R_d$, such that all the critical points of $g$ are in the basins of attraction of p...

Let $B$ denote the boundary of the Mandelbrot set (or, equivalently, the topological bifurcation set of the family $z\mapsto z^2+c$, $c\in\mathbb{C}$....

For nonconvex subsets of $\mathbb{R}$ and $\mathbb{R}^2$, is a set spectral if and only if it tiles by translations?...

Characterize the domains for which there exists a nonzero function whose integral vanishes over every congruent copy of the domain....

For $\phi(n)=\sup_{\deg p=n}\int_{|z|<1}|p'|/(1+|p|^2)\,dm$, let $\alpha=\limsup\log\phi(n)/\log n$. For a regular compact set $E$, define $\beta_E$ f...