Question
A system has this property if the limit as n goes to infinity of “log of M of n over log of n” is 1, where M of n is the time-averaged mean-squared displacement. For 10 points each:
[10h] Name this property that can be directly determined from a system’s time series in the 0-1 test. The most common test for this condition does not universally hold according to the phenomenon of Perron sign inversion.
ANSWER: chaos [accept word forms] (the most common test for chaos is the existence of a positive Lyapunov exponent)
[10m] Surprisingly, a dynamical system’s limit points can be one of these sets without it being chaotic. The Kaplan-Yorke conjecture relates a system’s Lyapunov exponents to the fractal dimension of these sets.
ANSWER: strange attractors
[10e] For a system to truly be chaotic, it must undergo mixing, have dense periodic orbits, and display sensitivity to the choice of these things, the values for a system at t = 0.
ANSWER: initial conditions [or initial states; or initial values]
<Fine, Physics>
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