Dynamical Systems     MATH 374

Homework Assignment #6 (Last One!)

Due Friday, April 4, 5:00 pm

All problem numbers refer to the primary course text by Robert 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 your work. A nonempty subset will be graded. You are encouraged to work on these problems with other classmates, and it is ok to use internet sources for help if it's absolutely necessary; however, the solutions you turn in should be YOUR OWN WORK and written in YOUR OWN WORDS.

Note: Please list the names of any students or faculty who you worked with on the assignment.

Strange Attractors
Read Strange Attractors, the fifth chapter of Gleick's book Chaos.

What is a strange attractor? In particular, what is the difference between an attractor and a strange attractor? Who were the two scientists to come up with the term? Who found the first strange attractor in their research before the term even existed?

Chapter 11 (pp. 151 - 153)
Problems:   1, 2, 3, 4

Hint: For problem #3, note that there is no assumption that F is continuous.

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

Additional Problem:
Prove the Transitivity Proposition, that is, prove that if f and g are topologically conjugate and f is toplogically transitive, then g is also topologically transistive. (See your class notes from 3/27 for hints and details.)