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.
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.
- Irwin, M. C. (2001), Smooth dynamical systems, Advanced Series in Nonlinear Dynamics, 17, World Scientific Publishing Co., Inc., River Edge, NJ, p. 47, doi:10.1142/9789812810120, ISBN 981-02-4599-8, MR 1867353.
- 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).
|This topology-related article is a stub. You can help Wikipedia by expanding it.|