Prolongation and prologational limit sets its topological dynamics

Abstract

In this short paper we try to state and prove some Impovtent theorem which we are given as an exercise to N.P. Bhatia and G.P. Szego and V.V. Stepanove & V.V. Nemytskii. Here we prove that every non-empty compact invariant set MCX contains some minimal sets. Now we also prove that a set MCX is minimal and only if for each x∈M,xR=M from these two rsults. We also prove that the omega limit set Ωx is minimal if for any two poihts y,z∈Ωx and any index a∈A There exists aτ∈R such that π(yτ)∈V_a (z).