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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