The understanding of discrete-state dynamical systems is important for application of chaos and interpretation of computer simulation with truncation errors, In this report, the asymptotic behavior of the invariant measure of discretized maps is studied. It is shown that the invariant measure converges to that of the continuous counterpart by interpreting the invariant measure with practically coarse observation precision, although it is not convergent in the strict sense. Accordingly, it is shown that the discretized maps typically have long orbits which reflect the ergodicity and the chaotic properties of the original maps. Moreover, the fractal structure inherent in the invariant measure of discretized maps are investigated.
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