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 smallest unstable Liapunov multiplier.