Semi-distality and related topics in generalized shift dynamical systems

	Semi-distality and related topics in generalized shift dynamical systems
Iranian Journal of Science
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 بهمن 1394
نوع مقاله: Regular Paper
شناسه دیجیتال (DOI): 10.22099/ijsts.2016.3575
نویسندگان
Fatemah Ayatollah Zadeh Shirazi^* ¹؛ Fatemeh Ebrahimifar¹؛ Bahman Taherkhani²
¹Faculty of Mathematics, Statistics and Computer Sience, College of Science, University of Tehran, Tehran, Iran
²Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-137, Tehran, Iran
چکیده
In the following text, we prove that the generalized shift dynamical system $(X^Gamma,sigma_varphi)$ with nonempty $Gamma$, ﬁnite discrete $X$ with at least two elements, and arbitrary map $varphi:GammatoGamma$ is semi-distal if and only if all points of $Gamma$ are quasi periodic points of $varphi$; moreover for countable $Gamma$, semi-distality and almost distality of $(X^Gamma,sigma_varphi)$ are equivalent. Also the following statements are equivalent: • The generalized shift $(X^Gamma,sigma_varphi)$ is pointwise minimal; • The generalized shift dynamical system $(X^Gamma,sigma_varphi)$ is distal; • The map $varphi:GammatoGamma$ is pointwise periodic (i.e, $Per(varphi)=Gamma$).
کلیدواژه‌ها
almost distal؛ generalized shift؛ minimal point؛ periodic point؛ semi-distal؛ transitive point

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