Chaos: Exact, Mixing and Weakly Mixing Maps

Mohammed Nokhas Murad Kaki

doi:doi:10.11648/j.pamj.20150402.11

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Chaos: Exact, Mixing and Weakly Mixing Maps

Mohammed Nokhas Murad Kaki

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 2)

Received: 19 December 2014 Accepted: 30 December 2014 Published: 11 February 2015

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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.

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.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Chaos, λ-Type Exact, Mixing, Weakly λ-Type Mixing, Conjugacy

References

[1]	H. Maki, Generalized Λ-sets and the associated closure operator, The Special Issue in Commemoration of Prof. Kazusada IKED’S Retirement, 1 Oct. (1986), 139-146.
[2]	F.G. Arenas, J. Dontchev and M. Ganster, On λ-sets and the dual of generalized continuity, Questions Answers Gen. Topology, 15 (1997), 3-13.
[3]	M. Caldas and S. Jafari, On some low separation axioms via λ--open and λ-closure operator, Rend. Circ. Mat. di Palermo, 54(2005), 195-208.
[4]	M. Caldas, S. Jafari and G. Navalagi, More on λ--closed sets in topological spaces, RevistaColombiana, 41 (2007), 355-369.
[5]	S. G. Crossley and S. K. Hildebrand, Semi topological properties, Fund. Math. 74(1972) 233-254
[6]	A. A. El-Atik, A study of some types of mappings on topological spaces, Master’s Thesis, Faculty of Science, Tanta University, Tanta, Egypt 1997.
[7]	Mohammed Nokhas Murad, New Types of Λ -Transitive Maps, International Journal ofResearch in Electrical and Electronics Engineering (ISTP-JREEE) ISSN: 2321-2667 Volume 2, Issue 5, Sept. 2013 pp.19-24
[8]	Mohammed Nokhas Murad, New types of chaotic maps on topological spaces, International Journal of Electrical and Electronic Science, American association for science and technology, (AASCIT) 2014; 1(1): 1-5, USA.

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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

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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

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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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@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}
}

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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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Author Information

Mohammed Nokhas Murad Kaki

Math Department, School of Science, Faculty of Science and Science Education, University of Sulaimani, Sulaymaniyah,Iraq

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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

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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

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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

Copy | 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}
}

Copy | Download

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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