Correlational properties of two-dimensional solvable chaos on the unit circle
This work provides incremental insights into the mathematical properties of chaotic systems, primarily relevant for researchers in theoretical physics or applied mathematics.
The paper tackled the problem of analyzing correlational properties of two-dimensional chaotic maps on the unit circle by deriving analytical forms of higher-order covariances and characteristic functions, finding that these are described by three types of two-dimensional Bessel functions and showing non-positive values for certain covariances.
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.