Homework #16

Reading: pg. 709-768

1. Show that the tent map is chaotic on [0,1]. (Hint: See HW #15, Problem 2.)

2. Show that the logistic map is topologically conjugate to Q(x)=x^2+c. (Hint: This can be done with a map of the form h(x)=ax+b.)

3. Find all points in code space on two symbols for which the shift map has a prime period 6 orbit.

4. Find the intervals A0, A00, A01, I0, and I1 for a=6 in the logistic map. Repeat for a=12.

5. Consider code space on three symbols {0,1,2}. Is the left shift map chaotic on it?

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