Homework should be turned in at the BEGINNING OF CLASS. 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 7 (pp. 80 - 81)
Problems: 1, 3, 5, 8, 9, 10, 11, 12, 13, 14, 16
Hint: For problem #16, there is an easy way and a hard way. The easy way is to use problem #4 from HW #4 to find a conjugate dynamical system we have already proven something about. The hard way is to draw the graphs of higher and higher iterates.
Let S be the itinerary map used to show that Q_c and the shift map are topologically conjugate. Prove that the inverse of the itinerary map S is continuous. (See class notes from 10/26 and 10/31 for details.)