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Section 2.9 Conjugacy

FigureĀ 2.3.1 and FigureĀ 2.6.1 show that the iterative behavior of the logistic family and the quadratic family are very similar. In a sense, they are identical in a sense that we'll make precise in this section. Furthermore, we'll show that the extreme cases \(f_{-2}(x)=x^2-2\) and \(g_4(x)=4x(1-x)\) are identical to the doubling map in this same sense and, therefore, chaotic.