Orbit closure
= Orbit closure
{title2=$\overline{\{T^n x:n\geq0\}}$}
The forward <orbit closure> of $x$ under a <continuous map> $T$ is the <closure> of its forward <orbit>. It is a closed forward-invariant set. If $T$ is invertible, one may instead consider the two-sided <orbit closure> using $n\in\mathbb Z$; the convention should be specified. For a <minimal point> of an invertible compact system the two closures agree.