Homework Assignment #2

Due Monday Sept 29^th.

Section 1.3 #16, 18

Section 2.2 #4ab

Section 2.4 #8, 9, 12, 14, 15 (optional overkill J : #16, 17) .

Standard results you probably proved in undergraduate analysis, are #7, 11

Section 2.5 Cantor Set #37, 38, 39 (the worksheet I gave you should help you do these problems).

Show that the Cantor set C is equivalent to the C intersect [6/9, 7/9]. (This is the fractal property of C – C is equivalent to a subset of itself. You could prove this for C intersect arbitrarily small intervals).

Section 2.6: #42, 43, 44, 46* (more challenging).

Dynamical Systems question: For the billiard map in the circle, examines issues of periodic orbits.

I encourage you to do the mini-problems I mention in class but I won’t collect them.