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