TITLE:
Chaos, Mixing, Weakly Mixing and Exactness
AUTHORS:
Mohammed Nokhas Murad Kaki
KEYWORDS:
θ-Chaotic Maps, θ-Mixing, Topological Exactness, Weak Mixing
JOURNAL NAME:
Open Access Library Journal,
Vol.5 No.6,
June
26,
2018
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.