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It is known that the Perron–Frobenius operators of piecewise expanding C transformations have an asymptotic periodicity of densities. On the other hand, external noise or measurement errors are unavoidable in practical systems, and therefore, every realistic mathematical model should be regarded as random iterations of transformations. The aim of this paper is to discuss the effects of randomization on the asymptotic periodicity of densities.

Noise-induced effect on asymptotic periodicity for random dynamical systems