Some Properties for a System with Dense Orbits

Abstract:

The point orbits under continuous self-maps on completely densely ordered linear ordered topological spaces (CDOLOTSs) are discussed. First, we point that the density of orbits implies the topological transitivity of the continuous self-map. Then, we give the necessary conditions for the density of the orbit under the even iterations. Such conditions are established on the fact that x(x is in L, L is a closed interval on a CDOLOTS) has a dense orbit under the continuous self-map.

• Periodical: Advanced Materials Research (Volumes 671-674)
• Pages: 1619-1623
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.671-674.1619
• Online since: March 2013
• Authors: Tian Xiu Lu, Pei Yong Zhu
• Keywords: Continuous Self-Maps, Dense Orbit, Periodic Points, Topological Transitive

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