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Unformatted text preview: the order , , 1 , , , 1 , , , , , 1 , 1 , 1 , 1 , 1 , 1 , , 1 , 1 , , Can you guess what choice of y was used? How sure can you be? (d) (5 pts) For a random y [0 , 1], are you more likely to get a repeating or a non-repeating sequence of 0s and 1s? (e) (5 pts) Consider a perturbation y of y . Show that for almost all y , | y n | = e n | y | , and nd the Liapunov exponent . 3. (10 pts) Write a program to simulate the Lorenz equations X =-PX + PY, Y =-XZ + rX-Y, Z = XY-bZ. For the standard parameters P = 10, b = 8 / 3, r = 28, convince yourself that a chaotic attractor exists which displays sensitive dependence on initial conditions. 1...
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This note was uploaded on 12/29/2011 for the course ME 215a taught by Professor Moehlis,j during the Fall '08 term at UCSB.
- Fall '08