7 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…

Consider basins of attraction in high-dimensional multistable dynamical systems, including the Kuramoto ring, where basin geometry may consist of a concentrated region near an attr…

Let $n$ identical oscillators evolve on a ring according to the Kuramoto model, and let the $q$-twisted state be the phase-locked state with winding number $q$. Wiley–Strogatz–Girv…

For $n>4$, consider the Kuramoto oscillator system on a cycle graph … with periodic boundary conditions. A $q$-twisted state is a phase-locked configuration of the form…

Let $A^*$ be the interconnection-strength parameter of an equilibrium, and let its basin of attraction be the set of initial data whose solutions converge to that equilibrium. Basi…

Fornæss–Stensønes conjecture. The abstract basin $\Omega$ of $(\varphi_n)$ is biholomorphic to $\mathbb C^q$.

Fornaess–Stensønes basin conjecture. The basin $\Omega$ is always biholomorphic to $\mathbb C^m$. A positive answer would imply a positive answer to Bedford's stable-manifold conje…