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Chaos, Mixing, Weakly Mixing and Exactness

DOI: 10.4236/oalib.1103773, PP. 1-7

Subject Areas: Dynamical System

Keywords: θ-Chaotic Maps, θ-Mixing, Topological Exactness, Weak Mixing

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Abstract

In this paper, new definitions of chaos, exact chaos, mixing chaos, and weak mixing chaos called θ-chaos, θ exact chaos, θ-mixing chaos are introduced and extended to topological spaces. Our purpose is to investigate other types of transitivity, chaos and mixing, because when we confirm not existence of θ-transitivity we confirm not existence of other types of transitive functions and its absence cannot find other types of transitivity. So the author must confirm the existence of this type of transitivity. We have proved that these chaotic definitions are all preserved under θ r-conjugation.

Cite this paper

Kaki, M. N. M. (2018). Chaos, Mixing, Weakly Mixing and Exactness. Open Access Library Journal, 5, e3773. doi: http://dx.doi.org/10.4236/oalib.1103773.

References

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[2]  Dontchev, J. and Maki, H. (1998) Groups of θ-Generalized Homeomorphisms and the Digital Line. Topology and Its Applications, 201-216.
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[4]  Kaki, M.N.M. (2015) Chaos: Exact, Mixing and Weakly Mixing Maps. Pure and Applied Mathematics Journal, Science PG, 4, 39-42.
[5]  Kaki, M.N.M. (2015) New Concepts of Alpha-Chaotic Maps. Journal of Multidisciplinary Engineering Science and Technology (JMEST), 2, 187-190.
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[8]  https://en.wikipedia.org/wiki/Group_action#cite_note-1

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