Consider the quadratic map Xk Xk1 2 C, where C > 0. (a) Prove that

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Consider the quadratic map Xk ¼ Xk1 2 þ C, where C > 0.

(a) Prove that C ¼ 0:25 is a bifurcation point.

(b) Find fixed points for C ¼ 0:125. Define what point is an attractor and what is its attraction basin for X > 0.

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