Dynamical Systems     MATH 374

Homework Assignment #6

Due Thursday, April 8, 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.

The Experimenter
Read The Experimenter, the seventh chapter of Gleick's book Chaos.

Describe the experiments carried out by Libchaber. In particular, describe them physically and discuss their aim. How does Libchaber's experiments in the "natural world" relate to material we've studied in this course? Why were his results so important to physicists?

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 topologically transistive. (See class notes from 3/23 for hints and details.)