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.
| DOI | 10.11648/j.pamj.s.2014030601.11 |
| Published in |
Pure and Applied Mathematics Journal (Volume 3, Issue 6-1, December 2014)
This article belongs to the Special Issue Mathematical Theory and Modeling |
| Page(s) | 1-6 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Chaos, α-Type Chaotic maps, α-Type Nonwandering Points, Transitive
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APA Style
Mohammed N. Murad Kaki. (2014). New Types of Chaos and Non-Wandering Points in Topological Spaces. Pure and Applied Mathematics Journal, 3(6-1), 1-6. https://doi.org/10.11648/j.pamj.s.2014030601.11
ACS Style
Mohammed N. Murad Kaki. New Types of Chaos and Non-Wandering Points in Topological Spaces. Pure Appl. Math. J. 2014, 3(6-1), 1-6. doi: 10.11648/j.pamj.s.2014030601.11
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Download@article{10.11648/j.pamj.s.2014030601.11,
author = {Mohammed N. Murad Kaki},
title = {New Types of Chaos and Non-Wandering Points in Topological Spaces},
journal = {Pure and Applied Mathematics Journal},
volume = {3},
number = {6-1},
pages = {1-6},
doi = {10.11648/j.pamj.s.2014030601.11},
url = {https://doi.org/10.11648/j.pamj.s.2014030601.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030601.11},
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.},
year = {2014}
}
TY - JOUR T1 - New Types of Chaos and Non-Wandering Points in Topological Spaces AU - Mohammed N. Murad Kaki Y1 - 2014/09/02 PY - 2014 N1 - https://doi.org/10.11648/j.pamj.s.2014030601.11 DO - 10.11648/j.pamj.s.2014030601.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 1 EP - 6 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2014030601.11 AB - 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. VL - 3 IS - 6-1 ER -
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