3 problems

A transcendental entire function is a transcendental holomorphic map $f:\mathbb{C}\to\mathbb{C}$; its order is the usual growth order of an entire function, and a Fatou component i…

Jordan-domain conjecture. Every bounded immediate attracting or parabolic basin of a transcendental entire function is a Jordan domain.

Completely invariant Fatou component conjecture. The number of completely invariant Fatou components of $f$ is at most two.