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.
be a Hausdorff space and
This means that for each neighborhood
[1] The set of recurrent points of
and is called the recurrent set of
Its closure is called the Birkhoff center of
,[2] and appears in the work of George David Birkhoff on dynamical systems.
[3][4] Every recurrent point is a nonwandering point,[1] hence if
is an invariant subset of the non-wandering set of
(and may be a proper subset).
This article incorporates material from Recurrent point on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
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