Abstract
The non-wandering set Ω(f) for a graph map f is investigated. It is showed that Ω(f) is contained in the closure of the set ER(f) of eventually recurrent points of f and ω-limit set ω(Ω(f)) of Ω(f) is contained in the closure of the set R(f) of recurrent points of f.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Block, L., Continuous maps of the interval with finite non-wandering set, Trans. Amer. Math. Soc., 1978,240(1):221–230.
Hosaka, H., Kato, H., Continuous maps of trees and non-wandering sets, Topology and Its Appl., 1997,81(1):35–46.
Ye, X. D., Non-wandering points and the depth of a graph map, J. Austral. Math. Soc. Ser. A, 2000,69:143–152.
Blokh, A. M., Dynamical systems on one-dimensional branched manifold I, Theor. Funktsiz Functional Anal. Prilozhen, 1986,46:8–18 (in Russian).
Coven, E. M., Nitecki, Z., Non-wandering sets of the powers of maps of the interval, Ergodic Theory Dynam. Systems, 1981,1:9–31.
Xiong, J. C., \(\Omega \left( {f\left| {_{\Omega \left( f \right)} } \right.} \right) = \overline {P\left( f \right)} \) for every continuous self-map f of the interval, Kexue Tongbao (English Ed.), 1983,28:21–23.
Author information
Authors and Affiliations
Additional information
The first author is supported by the Natural Science Foundation of the Committee of Education of Jiangsu Province (02KJB110008).
Rights and permissions
About this article
Cite this article
Gu, R., Sun, T. & Zheng, T. Non-wandering set of a continuous graph map. Appl. Math. Chin. Univ. 18, 477–481 (2003). https://doi.org/10.1007/s11766-003-0075-5
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11766-003-0075-5