2 problems

Berry–Klein's conjecture. At irrational times, the solution profiles of the periodic FLS equation have fractal dimension

Let $u$ solve the linear Schrödinger equation … with initial data $u(0,x)=f(x)\in L^2(\mathcal{M})$ on $\mathcal{M}=\mathbb{S}^d$ or $\mathbb{T}^d$, where $d\geq 2$. The higher-dim…