Dynamical Systems     MATH 374

Homework Assignment #7 (Last One!)

Due Thursday, April 22, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to the primary textbook 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.

Images of Chaos
Read Images of Chaos, the eighth chapter of Gleick's book Chaos.

Name the two mathematicians who proved rigorously that the Mandelbrot set M is connected, that is, there are no isolated "islands" or "bulbs" in M. What else did they prove about M? What field of mathematics did they utilize that had never been applied to dynamical systems before?

Chapter 14 (pp. 199 - 202)
Problems:   12, 15

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