| Peer-Reviewed

New Types of Chaos and Non-Wandering Points in Topological Spaces

Received: 7 July 2014     Accepted: 21 August 2014     Published: 2 September 2014
Views:       Downloads:
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.

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 6-1)

This article belongs to the Special Issue Mathematical Theory and Modeling

DOI 10.11648/j.pamj.s.2014030601.11
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), 2014. Published by Science Publishing Group

Keywords

Chaos, α-Type Chaotic maps, α-Type Nonwandering Points, Transitive

References
[1] Mohammed N. Murad Kaki, Topologically α - Transitive Maps and Minimal Systems Gen. Math. Notes, ISSN 2219-7184; Copyright © ICSRS Vol. 10, No. 2, (2012) pp. 43-53
[2] Mohammed N. Murad Kaki. Topologically α- Type Maps and Minimal α-Open Sets Canadian Journal on Computing in Mathematics, Natural Sciences, Engineering and Medicine Vol. 4 No. 2, (2013)
[3] N. Bourbaki, General Topology Part 1, Addison Wesley, Reading, Mass. 1966.
[4] M. Ganster and I.L. Reilly, Locally closed sets and LC-continuous functions, Internet. J. Math. Math. Sci. 12 (3) (1989), 417–424.
[5] Levine N., Semi open sets and semi continuity in topological spaces. Amer. Math. Monthly. 70(1963). 36-41.
[6] Bhattacharya P., and Lahiri K.B., Semi-generalized closed sets in topology. Indian J. Math. 29 (1987). 376-382.
[7] Levine N., Generalized closed sets in topology, Rend. Cire. Math. Paler no. (2) 19 (1970). 89-96.
[8] Ogata N., On some classes of nearly open sets, Pacific J. Math. 15(1965). 961-970.
[9] Andrijevie D., Some properties of the topology of α-sets, Math. Vesnik, (1994). 1 -10
[10] Mohammed N. Murad Kaki, New types of chaotic maps on topological spaces, International J. of Electrical and Electronic Science(AASCIT), Published online March 20, 2014, 1(1): 1-5
[11] F. Nakaoka and N. Oda: Some applications of minimal open sets, Internet Jr. Math. Math. Sci., 27(2001), no. 8 , 471-476.
[12] Kasahara S., Operation-compact spaces. Mathematica Japonica. 24 (1979).97-105.
[13] Rosas E., Vielina J., Operator- compact and Operator-connected spaces. Scientific Mathematica 1(2)(1998). 203-208.
[14] Maheshwari N. S., and Thakur S. S., On α-irresolute mappings, Tamkang J. Math. 11 (1980). 209- 214.
[15] http://www.scholarpedia.org/article/Minimal_dynamical_systems
Cite This Article
  • 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

    Copy | Download

    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

    Copy | Download

    AMA 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

    Copy | 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}
    }
    

    Copy | Download

  • 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  - 

    Copy | Download

Author Information
  • Math Dept., School of Science, University of Sulaimani, Sulaimani, Iraq

  • Sections