Complex dynamic phenomena usually occur in function iteration.Even simple functions and even the iteration of piecewise linear functions are very complex.It is usually very difficult to calculate the exact expression of n iterations of a piecewise linear function.In this paper,we consider the dynamic properties of N type mappings and define an index function for N type mappings.Using this index function,we give the exact expression of the n iterations of the mapping,and give the necessary and sufficient condition that the point is finally mapped to the fixed point at the n step.
N type mappingsiteration of n orderfinal fixed point
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