Characterizing loss of memory in a dynamical system

We propose here a new method to characterize the loss of memory with time in a chaotic system from a time series. This is done by introducing time-dependent generalized exponents. The asymptotic behavior can distinguish between chaotic systems which lose memory of the initial conditions completely, those which partially retain the memory, and those (borderline of chaos) which fully retain the memory. We give illustrative examples of the logistic and H\'enon maps.