Effects of randomization on asymptotic periodicity of nonsingular transformations

2014/09/12 by Hiroshi Ishitani, Ishitani, Hiroshi, Kensuke Ishitani +1
Mathematics · Physics and Astronomy · #28D99 (Primary) #37A30 #37A40 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #advanced mathematical theories #math.DS #msc:28D99 #msc:37A30 #msc:37A40

paper · pdf · doi:10.48550/arxiv.1409.3649

20 pages, 10 figures

openalex publication_date 2014/09/12 · arxiv created 2016/11/15 · arxiv updated 2016/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that the Perron--Frobenius operators of piecewise expanding C² transformations possess an asymptotic periodicity of densities. On the other hand, external noise or measurement errors are unavoidable in practical systems; therefore, all realistic mathematical models should be regarded as random iterations of transformations. This paper aims to discuss the effects of randomization on the asymptotic periodicity of densities.

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