Long-range correlation properties of area-preserving chaotic systems

This article shows numerically that the variance of the stretching exponents for two-dimensional chaotic area-preserving systems grows asymptotically as a linear function of time, although an intermediate anomalous power-law scaling may occur. This implies that the autocorrelation function of the stretching exponents is integrable. This result is a generic property of 2-d mixing systems generated by diffeomorphisms. The physical significance of the non-persistent anomalous behavior in the decay of fluctuations is briefly addressed.