3 problems

Let $\mathbb{T}^3$ be the three-dimensional torus, let $R_\alpha$ denote translation by $\alpha\in\mathbb{T}^3$, and let a natural coding mean a symbolic coding of the toral transl…

Measurable toral-translation conjecture. The dynamical system $(\Omega_{\sigma},S)$ is measurably equivalent to a toral translation.

Let $\alpha\in\mathbb{T}^d$ and let $\overline{D}(\alpha,N)$ denote the supremum of the discrepancy over the relevant class of boxes. Logarithmic discrepancy conjecture. For every…