Correlation properties of exactly solvable chaotic oscillators.

We derive exact expressions for the autocorrelation and cross-correlation functions of wave forms generated by two exactly solvable chaotic systems. For each system, an analytic expression exists for chaotic solutions, which we use to evaluate correlation integrals explicitly. For some specific parameter values, we calculate the mean and variance of the correlation functions averaged over all possible solutions. The mean autocorrelation is shown to decay at a rate equal to the Kolmogorov-Sinai entropy. All derived results are shown to agree with numerical calculations of the corresponding quantities.