Math 4/5027 - Nonlinear Dynamics and Chaos
Problem Set #3 - Spring 1998

Due March 2

Please do not postpone the assignment until the last minute! Remember you also need to identify a Challenge problem (one for undergraduates and two for graduate students) to work before the end of the semester. * marks problems for graduate students (extra credit for undergraduates).

  1. Reading. We will work through most of Chapter 3 in class. It is a collection of interesting ideas and techniques from both analysis and graph theory (no prior knowledge of graph theory is needed).

    Please to the following problems.

  2. Computing a Lyapunov exponent. Problem T3.2.
  3. *Checking conjugacy. Problem T3.6.
  4. *Periodic points under conjugacy. Problem T3.7.
  5. Analysis of a new map. Problem 3.1.
  6. A circle map. Problem 3.2.
  7. *Finding a conjugate map. Problem 3.3
  8. Analyzing a transition graph. Problem 3.9 (The problem should be interpreted to read that f is monotonic on intervals between the s.)

Just For Fun:

Two ice fishermen arrived at the circular Round Lake and set up their ice houses in opposite directions from the center, two-thirds of the distance from the center to the lake shore; in this way, they had ``control'' of equal areas of the lake (or had equal expectations of catching fish). A third fisherman arrived and the first two fishermen refused to move their ice houses. Can the third house be placed in such a way that all three fishermen have control of equal areas of the lake (or have equal expectations of catching fish)?


Thu Feb 18 05:51:03 MST 1999