MATH 225 Final: MATH 225 Amherst F13M225Final

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 225
• Professor: All

Document Summary

You can use the book, notes, class handouts and me. In- clude the mathematica output when you turn in the exam. Adapt the mathematica code in lab/hw #9, which is available at http://www. cs. amherst. edu/~dac/math225/lab9. nb (c) explain why s contains every point of the line segment connecting the lower left-hand corner of the fractal to its upper right-hand cor- ner. Hint: the ifs of part (a) gives f : k k such that for any. A k, f [n](a) s as n . Make a clever choice of a: [20 points] let gc : c c be de ned by gc(z) = z2 + c, where c c. The goal of this problem is to prove that. {c c | gc has a strictly attracting 2-cycle} = {c c | |c + 1| < 1. Here, a 2-cycle {z0, z1} is strictly attracting if |g c(z0)g (a) show that gc has a unique 2-cycle when c 6= 3 c(z1)| < 1.