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The closely spaced line segments in $R_1$ get spaced out more widely because $L$ expands distances along the unstable eigenline. These line segments get shorter because they are parallel to the stable …

This is a fun pair of exercises (the first one you mention is 3.2.9 and the second is 2.3.6a)! For 2.3.6a, recode to a $1$-block code $\phi$ on an irreducible edge shift $X$, suppose that $x, x' \in X …

Let $(X, \mathcal{B}, \mu, S)$ and $(Y, \mathcal{C}, \nu, T)$ be invertible probability-measure-preserving systems, with a measurable factor map $\pi: X \to Y$, i.e. $\pi \circ S = T \circ \pi$. Suppo …

Let $A$ be an irreducible nonnegative $N\times N$ integer matrix with constant row sum $D$. Let $A_1, \dots, A_D$ be nonnegative integer matrices, each with constant row sum $1$, such that $\sum_k A_k …

Context: I know essentially nothing about cohomology of any kind, but I have a problem involving classifying obstructions to extensions of certain maps or covers, and I have heard that cohomology is r …

Let $G$ be a countable amenable group and let $X,Y$ be subshifts with finite alphabet over $G$. Suppose that $h(X) = h(Y)$ (equal topological entropy). I am interested in continuous factor maps $\pi: …