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By means of Mathematica programming, we construct algorithms enabling us to evaluate various statistical quantities such as moments, correlation function matrices, and Lyapunov spectra in n-dimensional chaotic systems with discrete time steps. These algorithms are fundamentally based on a closed form of an integral representation of an approximate probability density, which holds as long as a Frobenius-Perron operator is asymptotically stable; in other words, the system is mixing. Therefore, our method is basically different from a usual box counting. After introducing our algorithms for calculating statistical quantities, we compare our method with the box counting by examining the Hénon map as a concrete example. Throughout our study, our emphasis is on the extent to which our method enables us to investigate the "hyperfine" structure of the Hénon attractor.
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