Dynamic Properties of Shift Mapping in Double Inverse Limit Space

From the discussion and research of dynamical system( X,f) is not difficult to see,since the mapping fis not necessarily a homeomorphism mapping,so,the system( X,f) is only half the power system of a topological space. In order to avoid its irreversibility arising in theoretical research difficulties,we introduce an associated shift maps on the inverse limit spaces,then,by using the inverse limit space of knowledge,the concept of the inverse limit space is extended to the double inverse limit space,and then in the non-compact metric space,continue to study f: X→X,g: X→X of double shift maps on the inverse limit spaces σf°σg: lim←( X,( f°g)) →lim←( X,( f°g)) some important dual dynamic characters.