Lyapunov Characteristics Indicators

When computing the Lyapunov Characteristics Indicators the attention is focused on the length of time necessary to get a reliable value of their limit, but very little importance has been given to the first part of the computation. Actually, this part was considered as a kind of transitory regime depending, among other factors, on the choice of an initial vector of the tangent manifold. 

Since the very beginning non graphical methods for the detection of chaos where implemented, taking into account the exponential divergence of nearby chaotic orbits (Froeschle 1970,b). The introduction, in a comprehensive way, of the Lyapunov Characteristic Exponents (LCEs hereafter) and a method for computing all of them (Benettin et al. 1980) made a major breakthrough for the characterization of chaos. Actually, the largest Lyapunov Exponent was already computed earlier (Froeschle 1970,b) but was called indicator of stochasticity since the works of the Russian mathematician where not known by the author (Froeschle 1984). 

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