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Complex Quadratic Polynomial




When it creates Discrete Dynamical System :

: z_{n+1} = P_c(z_n) \,

it is named Quadratic Map .

SPECIAL CASE

The Monic , Centered complex quadratic polynomial in one Variable z\, and one Parameter c\,

:P_c(z) = z^2 +c\,

is



A Critical Point of complex quadratic polynomial is a point ''z'' such that

: P_c'(z) = 0. \,

Since

: P_c'(z) = rac{d\bigl(P_c(z)\bigr)}{dz} = 2z =0

implies

: z = 0\,

we see that the only critical point of P_c(z) is the point z = 0\,.


REFERENCES



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