Dynamical Systems     MATH 374

Homework Assignment #7

Due Tuesday, Dec. 6, 5:00 pm

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 12 (pp. 161 - 163)
Problems:   1b, 1c, 2, 7, 8

Chapter 15 (pp. 218 - 220)
Problems:   2b, 2d, 3b, 3d, 5a, 5d, 5e, 5f, 8c, 8g, 9, 11

Chapter 16 (pp. 243 - 245)
Problems:   1, 5b, 5c

Hint: For #5c, try solving for the boundary first. You might want to review graphing in polar coordinates. The answer should look familiar.

Additional Problem:
Prove the Chain Rule for Schwarzian Derivatives given on page 156 of the text.