Definitions
Let
where and are complex-valued. (This is the complex quadratic mapping mentioned in the title.) This article explores the periodic points of this mapping - that is, the points that form a periodic cycle when is repeatedly applied to them.
is the -fold compositions of with itself = iteration of function or,
Periodic points of a complex quadratic mapping of period are points of the dynamical plane such that :
where is the smallest positive integer.
We can introduce a new function:
so periodic points are zeros of function :
which is a polynomial of degree
Read more about this topic: Periodic Points Of Complex Quadratic Mappings
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