Task id14110

Task id14110

Consider the Kadanov equation - a quadratic transformation f = 4lx(1 – x), which transforms the value x(n) into the subsequent x(n + 1) value as xn+1 = f(xn). Find analytically and graphically the fixed points of this transformation (a sequence of such points can be considered as a transformation with a period equal to one in the interval (0,1) of the values x and l). For what values of l are there two such points, and for what values is there one?

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