Recurrent point
= Recurrent point
{title2=$T^{n_j}x\to x,\quad n_j\to\infty$}
A point of a <dynamical system> is recurrent if some sequence of positive times tending to infinity returns its <orbit> arbitrarily close to the point. In a compact <metric space>, this is equivalent to the displayed condition. A periodic point is recurrent, but a recurrent point need not be periodic.