Characteristic Lyapunov vectors (CLVs) carry the information of the
tangent dynamics of a system: they are intrinsic, independent of the
scalar product, and covariant under time evolution. However, until
recently, it was not known how to compute CLVs efficiently in large
systems. In this talk I will review the methods recently available
to compute CLVs as well as the applications of these vectors to a
variety of practical and theoretical problems.
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