In this work, I studied a new class of topological λ-type chaos maps, λ-exact chaos and weakly λ-mixing chaos. Relationships with some other type of chaotic maps are given. I will list some relevant properties of λ-type chaotic map. The existence of chaotic behavior in deterministic systems has attracted researchers for many years. In engineering applications such as biological engineering, and chaos control, chaoticity of a topological system is an important subject for investigation. The definitions of λ-type chaos, λ-type exact chaos, λ-type mixing chaos, and weak λ-type mixing chaos are extended to topological spaces. This paper proves that these chaotic properties are all preserved under λr-conjugation. We have the following relationships: λ-type exact chaos⇒ λ-type mixing chaos ⇒ weak λ-type mixing chaos ⇒λ-type chaos.
| Published in | Pure and Applied Mathematics Journal (Volume 4, Issue 2) |
| DOI | 10.11648/j.pamj.20150402.11 |
| Page(s) | 39-42 |
| 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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Chaos, λ-Type Exact, Mixing, Weakly λ-Type Mixing, Conjugacy
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APA Style
Mohammed Nokhas Murad Kaki. (2015). Chaos: Exact, Mixing and Weakly Mixing Maps. Pure and Applied Mathematics Journal, 4(2), 39-42. https://doi.org/10.11648/j.pamj.20150402.11
ACS Style
Mohammed Nokhas Murad Kaki. Chaos: Exact, Mixing and Weakly Mixing Maps. Pure Appl. Math. J. 2015, 4(2), 39-42. doi: 10.11648/j.pamj.20150402.11
AMA Style
Mohammed Nokhas Murad Kaki. Chaos: Exact, Mixing and Weakly Mixing Maps. Pure Appl Math J. 2015;4(2):39-42. doi: 10.11648/j.pamj.20150402.11
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Download@article{10.11648/j.pamj.20150402.11,
author = {Mohammed Nokhas Murad Kaki},
title = {Chaos: Exact, Mixing and Weakly Mixing Maps},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {2},
pages = {39-42},
doi = {10.11648/j.pamj.20150402.11},
url = {https://doi.org/10.11648/j.pamj.20150402.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150402.11},
abstract = {In this work, I studied a new class of topological λ-type chaos maps, λ-exact chaos and weakly λ-mixing chaos. Relationships with some other type of chaotic maps are given. I will list some relevant properties of λ-type chaotic map. The existence of chaotic behavior in deterministic systems has attracted researchers for many years. In engineering applications such as biological engineering, and chaos control, chaoticity of a topological system is an important subject for investigation. The definitions of λ-type chaos, λ-type exact chaos, λ-type mixing chaos, and weak λ-type mixing chaos are extended to topological spaces. This paper proves that these chaotic properties are all preserved under λr-conjugation. We have the following relationships: λ-type exact chaos⇒ λ-type mixing chaos ⇒ weak λ-type mixing chaos ⇒λ-type chaos.},
year = {2015}
}
TY - JOUR T1 - Chaos: Exact, Mixing and Weakly Mixing Maps AU - Mohammed Nokhas Murad Kaki Y1 - 2015/02/11 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.20150402.11 DO - 10.11648/j.pamj.20150402.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 39 EP - 42 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20150402.11 AB - In this work, I studied a new class of topological λ-type chaos maps, λ-exact chaos and weakly λ-mixing chaos. Relationships with some other type of chaotic maps are given. I will list some relevant properties of λ-type chaotic map. The existence of chaotic behavior in deterministic systems has attracted researchers for many years. In engineering applications such as biological engineering, and chaos control, chaoticity of a topological system is an important subject for investigation. The definitions of λ-type chaos, λ-type exact chaos, λ-type mixing chaos, and weak λ-type mixing chaos are extended to topological spaces. This paper proves that these chaotic properties are all preserved under λr-conjugation. We have the following relationships: λ-type exact chaos⇒ λ-type mixing chaos ⇒ weak λ-type mixing chaos ⇒λ-type chaos. VL - 4 IS - 2 ER -
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