4 problems

Let $(X,T)$ be a Toeplitz flow with period structure $(p_k)$, and let $(X,S)$ be a bounded speedup of $(X,T)$ with orbit number $c$. For the Kakutani–Rokhlin partition…

Let $(X,T)$ be a Toeplitz flow and let $(X,S)$ be a minimal bounded speedup, with $S(x)=T^{p(x)}(x)$. Suppose a Kakutani–Rokhlin partition has a common cyclic orbit permutation and…

Let $(X,T)$ be a Toeplitz flow, meaning a symbolic, minimal, almost one-to-one extension of an odometer, and let $(X,S)$ be its minimal bounded speedup, where $S(x)=T^{p(x)}(x)$ fo…

Let $(X_1,\mathbf{T}_1)$ be a minimal $\mathbb{Z}^d$-Cantor system and let $(X_2,\mathbf{T}_2)$ be a higher-dimensional odometer action. A $\textsf{{C}}$-speedup of…