Homework # 5
Due Oct. 23 at the beginning of class
T4.2
T4.3
Comp. Exp. 4.1 Modify my 1D code cantorifs.m to make your code. You do not need to hand in the plot.
This should be easy. Then replace the map given by what you deduce in T4.3. Hand in
your code
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Math 53: Chaos! 2009: Midterml
2 hours, 54 points total, 6 questions worth various points (proportional to blank space)
I
1. {9 points] Consider the two-dimensional map x + Ax. p FAY A. [Nu-hr MA?)
3 If A = 1 _1/2 , de
Homework # 4
Due Oct. 16 at the beginning of class
Comp. Exp. 3.1 You can combine bits of code from Homework 1 and from Comp. Exp. 2.2 from last
homework to make this Lyapunov exponent vs. a plot. Use ne steps in a, e.g., 103 , to
see the jagged quality.
Homework # 7
Due Nov. 7 at the beginning of the exam time.
5.2
A Compute the Lyapunov exponents of the baker map
B (x, y ) =
(x/2, 2y (mod 1)
(x + 1)/2, 2y (mod 1)
for y 1/2
for y < 1/2
acting on the unit square. What does the sum of the Lyapunov exponent
Homework # 6
Due Oct. 30 at the beginning of class
Comp. Exp 4.3 Write a code which plots the Julia set on a grid, for the c value from the last homework,
on the domain |Rez0 | < 1.5 and |Imz0 | < 1.5 with resolution of 0.01. Use at least 200
iterations.
Homework # 3
Due Oct. 9 at the beginning of class
2.3 Please also state if the xed points are hyperbolic or not.
A. Find the slight subtlety in the proof that AB and BA have the same eigenvalues. This
underlies the fact that stability is the same independ
Homework # 1
Due September 25 at the beginning of class
Please collaborate on ideas, but write up individually. If still stuck, come to oce hours
or email me. Unless labeled A, B, etc, problems are from Alligood-Sauer-Yorke. Remember
to show your working/
Homework # 2
Due Oct. 2 at the beginning of class
Please collaborate on ideas, but write up individually. If still stuck, come to oce hours
or email me. Unless labeled A, B, etc, problems are from Alligood-Sauer-Yorke. Remember
to show your working/reason