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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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آمار تعداد مشاهده مقاله: 909 |
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