(a) Let T be the function T : [0, 1] [0, 1] defined by T (x)...

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(a) Let T be the function T : [0, 1] → [0, 1] defined by T (x) =

7 4 x, 0 ≤ x < 1 2 , 7 4 (1 − x), 1 2 ≤ x ≤ 1.

Determine the fixed points of periods one, two, and three.

[12]

(b) Determine the fixed points of periods one and two for the complex mapping zn+1 = z2n

− 3.

Determine the stability of the fixed points of period one.

[8]

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