On the Invariance Property for S−Flows in Ttopological Dynamics System
Abdulkafi A. Al-Rafaei1, Amin Saif2
1Abdulkafi A. Al-Rafaei, Faculty of Applied Sciences, Thmar University, Thmar, Yemen.
2Amin Saif, Faculty of Applied Sciences, Taiz University, Taiz, Yemen.
Manuscript received on Novmeber 14, 2018. | Revised Version Manuscript Received on 20 November, 2018. | Manuscript published on December 20, 2018. | PP: 7-9 | Volume-2 Issue-6, December 2018 | Retrieval Number: F0080122618/19©BEIESP
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© The Authors. Published by Lattice Science Publication (LSP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this paper, we start by giving an equivalence relation on a topological space X which correspond, under the action of a topological monoid S, to the S−invariant control sets for control systems. Then we give some results about the S−invariant classes for this relation. The conditions for the existence and uniqueness of relative S−invariant classes will be given.
Keywords: Topological monoid; S−flow; S−phase flow. AMS classification: 06F05, 76D55.