Unformatted text preview: the order , , 1 , , , 1 , , , , , 1 , 1 , 1 , 1 , 1 , 1 , , 1 , 1 , , Â· Â· Â· Can you guess what choice of y was used? How sure can you be? (d) (5 pts) For a random y âˆˆ [0 , 1], are you more likely to get a repeating or a nonrepeating sequence of 0â€™s and 1â€™s? (e) (5 pts) Consider a perturbation Î´y of y . Show that for almost all y ,  Î´y n  = e n Î›  Î´y  , and ï¬nd the Liapunov exponent Î›. 3. (10 pts) Write a program to simulate the Lorenz equations Ë™ X =PX + PY, Ë™ Y =XZ + rXY, Ë™ Z = XYbZ. For the â€œstandard parametersâ€ 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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 Fall '08
 Moehlis,J
 Chaos Theory, pts, 5 pts, 10 pts, Applied Dynamical Systems

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