New Types of Chaos and Non-Wandering Points in Topological Spaces
Pure and Applied Mathematics Journal
Volume 3, Issue 6-1, December 2014, Pages: 1-6
Received: Jul. 7, 2014; Accepted: Aug. 21, 2014; Published: Sep. 2, 2014
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Author
Mohammed N. Murad Kaki, Math Dept., School of Science, University of Sulaimani, Sulaimani, Iraq
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Abstract
In this paper, we will define a new class of chaotic maps on locally compact Hausdorff spaces called α-type chaotic maps defined by α-type transitive maps. This new definition coincides with Devaney's definition for chaos when the topological space happens to be a metric space. Furthermore, we will study new types of non-wandering points called α-type nonwandering points. We have shown that the α-type nonwandering points imply nonwandering points but not conversely. Finally, we have defined new concepts of chaotic on topological space. Relationships with some other type of chaotic maps are given.
Keywords
Chaos, α-Type Chaotic maps, α-Type Nonwandering Points, Transitive
To cite this article
Mohammed N. Murad Kaki, New Types of Chaos and Non-Wandering Points in Topological Spaces, Pure and Applied Mathematics Journal. Special Issue: Mathematical Theory and Modeling. Vol. 3, No. 6-1, 2014, pp. 1-6. doi: 10.11648/j.pamj.s.2014030601.11
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