  This article investigates correlational properties of two-dimensional chaotic
maps on the unit circle. We give analytical forms of higher-order covariances.
We derive the characteristic function of their simultaneous and lagged ergodic
densities. We found that these characteristic functions are described by three
types of two-dimensional Bessel functions. Higher-order covariances between x
and y and those between y and y show non-positive values. Asymmetric features
between cosine and sine functions are elucidated.
