In mathematics, a recurrent point for a function f is a point that is in its own limit set by f. Any neighborhood containing the recurrent point will also contain (a countable number of) iterates of it as well.

Definition

be a Hausdorff space, i.e.-limit set. This means that for each neighborhood.

and is called the recurrent set. Its closure is called the Birkhoff center, and appears in the work of George David Birkhoff on dynamical systems.

Every recurrent point is a nonwandering point, is a homeomorphism is compact is an invariant subset (and may be a proper subset) and it's already closed.

References