5 problems

Let $\{\phi_t\}_{t\geq 0}$ be a semigroup of holomorphic self-maps of the upper half-plane $\mathbb{H}$, and consider the set of slopes associated with its orbits in the continuous…

Let $(\phi_t)_{t\geq 0}$ be a parabolic semigroup of holomorphic self-maps of the unit disc, and let $v^T_\phi(t)$ denote its tangential speed. Bracci's conjecture. The function…

Forward-orbit stable-basin conjecture. For each component $U$ of $F(S)$, there is a stable basin $V$ for $S$ lying in the forward orbit of $U$ that has cofinite index in $S$.

Stable-basin conjecture. Then a stable basin $U$ has cofinite index in $S$.

Let $(\varphi_t)\subset\operatorname{Hol}(\mathbb D,\mathbb D)$ be a hyperbolic or parabolic one-parameter semigroup with Denjoy–Wolff point $\tau\in\partial\mathbb D$. For…