Eighth Homework Set Answers

4. (a) For the s = 2 tent map the fixed point equation T(x*) = x* becomes

2 - 2x* = x*

Solving gives x* = 2/3.

(b) Here are the graphical iteration plots locating the four points.

(c) First, observe a is the nonzero fixed point x*, so a = 2/3.

Next, 2/3 = T(b) = 2b, so b = 2/6 = 1/3.

Then, 2/3 = T2(c) = 2(2c) = 4c, so c = 2/12 = 1/6.

Finally, 2/3 = T2(c) = 2(2 - 2d) = 4 - 4d, so 4d = 4 - 2/3 and d = 5/6.

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