7 problems

Let $\bbS^2=\bbR^2/\bbZ^2$ be partitioned into four rectangles as the product of partitions $\bbS=\bbS^1=\bbR/\bbZ=\delta^x_1\cup\delta^x_2$ and $\delta^y_1\cup\delta^y_2$. Conside…

Let $\mathcal{V}$ be the parameter space of finite-type double rotations with a fixed partition, and let the associated map have an attractor. The attractor is semi-continuous with…

Let $\mathcal{V}$ be the parameter space of pairs ${v_0,v_1}$, with a fixed partition, for which the double-rotation map $f_{v_0,v_1}$ on a two-dimensional torus is of finite type.…

Let $\mathbb{T}$ be a two-dimensional torus, let $Rsubseteqmathbb{T}$ be a fixed partition region, and let $v_0,v_1inmathbb{R}^2$. The associated double rotation is the map…

Let $\mathcal{W}$ be the space of translation vectors for which the associated piecewise translation map with fixed partition $\mathcal{B}$ is of finite type, and let $X_a$ be the…

Let $g=(A_1A_2)^2$ with $s$ irrational, and let the associated double lattice PET from the compactification theorem be defined on a compactified space with invariant foliation. Den…

Let $R_+$ denote the positive real numbers, and let $A_s=(R_{1,0}R_{s,0})^2$ be the alternating grid system. Let $Q_s$ be the square of $G_{s,0}$ whose bottom-left vertex is the or…