Applied Physics 461b/861b

COMPUTATIONAL PHYSICS

Assignment 4

due Friday, February 14, 1997

Reading

  1. Gould and Tobochnik Chapter 6.1-6.5.
  2. ``Strange attractors,'' by Douglas R. Hofstadter, Scientific American 245 (11), 22 (1981).

1. Stable and unstable fixed points, bifurcation and period doubling

Write your own Fortran program to iterate the map x_{n+1}=4 r x_n (1-x_n), and do Problem 6.1 a, b and c. Graphical presentation of the output is optional.

2. Iterated nonlinear maps and floating point arithmetic

Problem 6.3 b.

3. Windows of periodic behavior in the chaotic regime

Problem 6.5 a, b and c. Part b is a graphical interpretation of the period 3 behavior, and I suggest making the necessary plots with Mathematica.

4. The Feigenbaum constant

Make sure you understand the definition of delta, and do Problem 6.6 a.

5. The Lyapunov exponent

Problem 6.9 a, b and c. Part c is a logical continuation of Problem 6.3b, assigned above.