4 problems

Let $\phi$ be an analytic univalent self-map of the disk, and consider backward-iteration sequences with bounded hyperbolic steps (BISBS) for $\phi$, classified according to whethe…

Let $N\ge1$ and let $F:\mathbb D^N\to\mathbb D^N$ be holomorphic and without fixed points. Write $F^{\circ n}$ for the $n$-fold iterate and let $\pi_j(z)=z_j$ be projection onto th…

Let $\Omega\subset\mathbb C^N$ be a bounded convex domain. Visibility–Denjoy–Wolff conjecture. Then $\Omega$ is visible if and only if it enjoys the Denjoy–Wolff property. The conj…

Let $\Omega\subset\mathbb C^N$ be a bounded convex domain whose boundary contains no non-trivial analytic discs. A sequential horosphere is a set of the form … where…