5 problems

Let $f_1,f_2,\ldots$ be a sequence of automorphisms of $\mathbb{C}^k$. Assume that there exist constants $0<a<b<1$ such that, for every $n$ and every $z$ in the unit ball, one has…

Michael's conjecture. The existence of sequences of Fatou-Bieberbach domains having the properties needed in the reduction of Michael's conjecture should be established.

Strong Fatou–Bieberbach approximation conjecture. For each $r\in(0,1)$, there exist a Fatou–Bieberbach domain $\Omega_r$ and a sequence…

Fatou–Bieberbach approximation conjecture. For every $r\in(0,1)$, there exists a domain $\Omega_r\subseteq{\mathbb{C}^n}$ biholomorphic to ${\mathbb{C}^n}$ such that

Fatou–Bieberbach realization conjecture. There exists a Fatou–Bieberbach domain $\Omega\subseteq{\mathbb{C}^n}$ with $D\subseteq\Omega$ such that $(D,\Omega)$ is a Runge pair. This…