Dynamical Systems     MATH 374

Homework Assignment #5

Due Wednesday, Nov. 2, START of Class

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.

Additional Problem:
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.)