Homoclinic points of algebraic $\mathbb {Z}^d$-actions
Homoclinic points of algebraic $\mathbb {Z}^d$-actions
Let $\alpha$ be an action of $\mathbb Z^d$ by continuous automorphisms of a compact abelian group $X$. A point $x$ in $X$ is called homoclinic for $\alpha$ if $\alpha ^{\mathbf n}x\to 0_X$ as $\|\mathbf n\|\to \infty$. We study the set $\Delta _{\alpha }(X)$ of homoclinic points for $\alpha$, which is …