About Upgrade And Mapping Degree Of Self-mapping For Torus In The Topological Space

In this paper,we studied two questions in topological dynamics.First,in 1992,Zhang Jingzhong and Xiong Jincheng determined upgrade and mapping degree of continuous self-mapping f on cirle continuous S~1 in〈〈Iterative Function and Dynamical Systems of One-dimension〉〉.Considering f:T~2→T~2 is a contionuous self-mapping of tours,using character of covering spaces and upgrade mapping,one-dimensional continuous self-mapping of circle is extended to two-dimensional contionuous self-mapping of tours.In part two,in 1979,Jiang Zehan gave the relation between fixed points and isolated fixed points of contionuous self-mapping of circle,and determined fixed points of upgrade mapping on circle.In this paper,the relation between fixed points and isolated fixed points of contionuous self-mapping of tours and fixed points of upgrade mapping are obtained.