All problem numbers refer to the course text by 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 ALL YOUR WORK. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.

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

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

Problems: 3, 4, 6, 8, 11, 16, 20, 24

**Hint:** For problem #20, there are two different approaches. One is to use the
graphs of the higher iterates of D(x) which you computed in HW#2, Ch. 3, Exercise 13
and prove that D(x) satisfies all three properties of chaos directly. The second approach
is to use binary notation and see what map D(x) reminds you of.

**Chapter 11 (pp. 151 - 153) **

Problems: 1, 2, 3, 4

**Hint:** For problem #3, note that there is no assumption that **F** is continuous.

**Additional Problem:**

Prove the Transitivity Proposition, that is, prove that if f and g are topologically conjugate
and f is toplogically transitive, then g is topologically transistive.
(See class notes from 11/7 for hints and details.)