Abstract: The investigations about chaos, at tractor and strange at tractor are main subjects in non-linear analysis. Under the framework of pansystems methodology, reference [1] discussed these problems and introduced the concepts of panchaos, panattractor and strange panattractor. These concepts omit ted the condition of continuity, compactness, etc. and put stress on the properties of binary relations on a set. A certain obtained result indicates that panchaos, panattractor and strange panattractor correspond respectively to fixed subsets of certain pansys tems operators. This paper continues the investigation of [1,2], discusses the existence of these pansystems fixed subsets, their construction and interrelations.