Liapunov Multipliers and Decay of Correlations in Dynamical Systems

The essential decorrelation rate of a hyperbolic dynamical system is the decay rate of time-correlations one expects to see stably for typical observables once resonances are projected out. We define and illustrate these notions and study the conjecture that for observables in $C^1$, the essential decorrelation rate is never faster than what is dictated by the {\em smallest} unstable Liapunov multiplier.