Iteration
Given an, one cannot always deduce the analytic form of, which means the nth iteration of . (The superscript can be extended to negative number referring to the iteration of the inverse of if the inverse exists.) But there is one easier case, in which .
In such case, one has
- ,
where
- and .
So by induction,
can be obtained, where can be easily computed as
- .
Finally, we have
- ,
in the case of .
See Topological conjugacy for more detail about such relationship between f and g. And see Complex quadratic polynomial for the chaotic behavior in the general iteration.
Read more about this topic: Quadratic Function
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