All problem numbers refer to the primary course text by Robert Devaney. Unless otherwise indicated, all parts of a problem (a), (b), etc. should be completed. You should write up solutions neatly to all problems, making sure to show your work. A nonempty subset will be graded. You are encouraged to work on these problems with other classmates, and it is ok to use internet sources for help if it's absolutely necessary; however, the solutions you turn in should be YOUR OWN WORK and written in YOUR OWN WORDS.

** Note: ** Please list the names of any students or faculty who you worked with on the assignment.

**Chapter 7 (pp. 80 - 81) **

Problems: 3, 5, 9, 10, 12, 13

**Chapter 10 (pp. 130 - 132) **

Problems: 3, 4, 6, 8, 16, 20

**Hint:** For problem #20, there are two different approaches. One approach is to use the
graphs of the higher iterates of **D(x)** that you computed for HW#1, Ch. 3, Exercise 13,
and prove that **D(x)** satisfies all three properties of chaos directly. The second approach
is to use binary notation for **x** and **D(x)** and see what map **D(x)** reminds you of.

**Additional Problem:**

Let **S** be the itinerary map used to show that **Q _{c}** and the shift map