Limit sets in product of semi-dynamical systems (Q1301931)

The paper is in continuation to the paper \textit{S. S. Prasad} and \textit{A. Kumar} [ibid. 7, No. 1, 181-185 (1984; Zbl 0562.54061)] and deals with the study of stability properties of products of semi-dynamical systems. A typical result is the following (Theorem 3.7): Let \((x_{\alpha },\Pi _{\alpha }),\alpha \in I,\) be a family of Lagrange stable and distal s.d.s. (semi-dynamical systems) and \((X,\Pi)\) be the product of s.d.s. Let \(x\in X\) and \(x=\left\{ x_{\alpha }\right\} .\) A motion \(\Pi (x,t)\) is Poisson stable in \((X,\Pi)\) if and only if \(\Pi _{\alpha }(X_{\alpha },t)\) is Poisson stable in \((X_{\alpha },\Pi _{\alpha }) \) for each \(\alpha \in I.\)