Pelczar, Andrzej Limit sets and prolongations in pseudo-processes. (English) Zbl 0675.54038 Zesz. Nauk. Uniw. Jagielloń. 860, Acta Math. 27, 169-186 (1988). This paper is concerned with the behaviour of limit sets and prolongations and stability for pseudo-processes. (X,G,H,\(\mu)\) is a pseudo-process if G is an abelian semigroup, H is a subsemi-group containing the neutral element 0, X is nonempty set and \(\mu\) maps \(G\times H\times H\) into X such that \(\mu (g,x,0)=x\) (g\(\in G\), \(x\in X)\) and \(\mu (g+h,\mu (g,x,h),k)=\mu (g,x,h+k)\) (g\(\in G\), \(x\in X\), \(h,k\in H)\). The author considers the case G being the reals, H the non-negative reals, and X a compact metric space. Pseudo-processes are a generalisation of abstract dynamical systems. The author defines various stability-like conditions for pseudo-processes and defines positive “orbits” and limit sets in a natural way. It is shown, for example, that limit sets are closed and connected (under appropriate assumptions). The main theorems relate the stability conditions to the upper semi-continuity of (point of set) maps from points to their appropriate limit sets. These ideas and results are then extended to prolongations. Reviewer: M.Sears MSC: 54H20 Topological dynamics (MSC2010) Keywords:behaviour of limit sets; prolongations; stability for pseudo-processes; stability-like conditions; upper semi-continuity PDFBibTeX XMLCite \textit{A. Pelczar}, Zesz. Nauk. Uniw. Jagielloń. [...], Acta Math. 860(27), 169--186 (1988; Zbl 0675.54038)