Table of Contents
Journal of Chaos
Volume 2013, Article ID 181238, 4 pages
http://dx.doi.org/10.1155/2013/181238
Research Article

Unstable Manifolds of Continuous Self-Mappings

1School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2Department of Mathematics, Sichuan University of Science and Engineering, Zigong 643000, China

Received 5 March 2013; Revised 16 May 2013; Accepted 23 May 2013

Academic Editor: Tao Xiang

Copyright © 2013 Tianxiu Lu and Peiyong Zhu. 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

Unstable manifolds of continuous self-mappings on completely densely ordered linear ordered topological spaces (CDOLOTS) are discussed. Let be a continuous self-map. First, the interval with endpoints of two adjacent fixed points is contained in the unilateral unstable manifold of one of the endpoints. Then, by using the above conclusion, we prove that periodic points of not belong to the unstable manifold of their iteration points of (for some ), unless the iteration points are themselves.