Generalizations And Applications Of Stefan Square Root

This paper discusses the extension and application of Stefan square root and Stefanmap. It introduces the concepts of “square root”construction method,Stefan squareroot,Stefan map,and explains the basic theory and corresponding main results.It givesfour kinds of generalized definition of Stefan square root,and gives two kinds of thedefinition of the generalized form of the Stefan map and gives specific examples.Thesegeneralized definition provide more extensive theoretical basis for the construction ofSarkovskii section.The paper summarizes the theory of perfect map which is given byprofessor Sheng Zhongping. The theory of perfect map proposes the definition ofperfect map,and gives the necessary conditions for the existence of perfect map,andproves the uniqueness of the perfect map,and uses iterated function systems to drawthe image of the perfect map.Simultaneously,the paper also prove the periodic pointsof perfect map are fixed points.The periodic points set of perfect map is Cantor set andopen midpiont set.The perfect map theory perfect the theory system of Stenfan squareroot,at the same time,it is an example of fractal interpolation.