In order to calculate Lyapunov Spectrum from a time series, one need to calculate Local Jacobian's of the point of interest, on the attractor. (According to Nonlinear Time Series Analysis, Kantz & Schreiber).
Eckmann et al and Sano & Sawada also suggested the tangent space methods to estimate the Lyapunov Spectrum.
I need basic understand-ability of these methods. If anyone working on find the Lyapunov Spectrum, help in above issues.
Thank you everyone.
I don't know that but I suppose you know https://www.pks.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/node28.html that Google mentioned among the first links. A program lyap_spec is mentioned.
If you make use of Matlab and need to evaluate accurate Jacobians of a function there is a small toolbox due to John D'Errico and used for example in papers by Aït-Sahalia. Of course it does not work on the data themselves but on a likelihood function. In case you are interested, please contact me or look in my slides where it is mentioned. The purpose is to be more accurate than simple divided differences, i.e. approximating f'(x) by (f(x+h) - f(x))/h for a moderately small h.
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