Diapositiva PPT

• For “good” dynamical systems, the Lyapunov exponent at

large times converges to a single value for almost all of the

initial conditions: P(l,t) » t 1/2 exp(-G(l)t ) , t® ¥

• But there are initial conditions forming fractal sets of zero

measure at which l takes different values.

At these places, since a = b/ l , a takes nonstandard values.

• The fractal dimension of these sets can be obtained from the

pdf of the finite-time Lyapunov exponent values as

D(l) =2 - G(l)/ l

MULTIFRACTALITY

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