In mathematics, a recurrent point for a function f is a point that is in the limit set of the iterated function f. Any neighborhood containing the recurrent point will also contain (a countable number of) iterates of it as well.
The set of recurrent points of is often denoted and is called the recurrent set of . Its closure is called the Birkhoff center of , and appears in the work of George David Birkhoff on dynamical systems.
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- Hart, Klaas Pieter; Nagata, Jun-iti; Vaughan, Jerry E. (2004), Encyclopedia of general topology, Elsevier, p. 390, ISBN 0-444-50355-2, MR 2049453.
- Coven, Ethan M.; Hedlund, G. A. (1980), " for maps of the interval", Proceedings of the American Mathematical Society 79 (2): 316–318, doi:10.2307/2043258, MR 565362.
- Birkhoff, G. D. (1927), "Chapter 7", Dynamical Systems, Amer. Math. Soc. Colloq. Publ. 9, Providence, R. I.: American Mathematical Society. As cited by Coven & Hedlund (1980).
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