Finite-time Lyapunov exponents correction

Now we present our novel method for computing accurate values of finite-time Lyapunov exponents and vectors, by correcting the finite-time error in [24], To this end, we construct a sequence of refinements U 1], d, r, and Vik] (k = 0,1,2,...) satisfying... 

Nam et al. (1999) have shown that the intermittent inhomogeneity of the dispersion rate also leads to a correction for the exponent of the power spectrum (6.21). The power spectrum can be considered as a superposition of contributions from wavepackets of concentration fluctuations associated to trajectories that have experienced different history of dispersion rates distributed according to (6.37). The proportion of wavepackets with a cumulative dispersion rate At after time t decays as exp(—G(X)t). Thus, the contribution of wavepackets for which the finite-time Lyapunov exponent has a particular value A satisfies Eq. (6.18) in a generalized form... 

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