Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 132985, 7 pages
http://dx.doi.org/10.1155/2011/132985
Research Article

Topological Entropy and Special 𝜶 -Limit Points of Graph Maps

Taixiang Sun, Guangwang Su, Hailan Liang, and Qiuli He

College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China

Received 11 December 2010; Revised 4 February 2011; Accepted 2 March 2011

Academic Editor: M. De la Sen

Copyright © 2011 Taixiang Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let 𝐺 a graph and 𝑓 ∶ 𝐺 → 𝐺 be a continuous map. Denote by ℎ ( 𝑓 ) , 𝑅 ( 𝑓 ) , and S A ( 𝑓 ) the topological entropy, the set of recurrent points, and the set of special 𝛼 -limit points of 𝑓 , respectively. In this paper, we show that ℎ ( 𝑓 ) > 0 if and only if S A ( 𝑓 ) − 𝑅 ( 𝑓 ) ≠ ∅ .