Bildik NecdetInc Mustafa2024-07-222024-07-2219991300686Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/20645In this paper, the definitions and the theorems concerning with the invariant sets, w- and α-limit sets are given and proved in the new Dynamical Systems. By using of the definition of P+ and P- stability, some remarkable unknown results are obtained. Finally, the definition of Dynamical Isomorphism and Dynamical Homeomorphism are given and related original theorems are presented and proved.EnglishAll Open Access; Gold Open AccessMathematical modelsSet theorySystem stabilityTheorem provingDynamical homeomorphismDynamical isomorphismInvariant setsMathematical morphologyArticle10.3390/mca4020189