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Entropy of random chaotic interval map with noise which causes coarse-graining

2012/05/09 by Kouji Yano, Yano, Kouji
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.1205.1848

openalex publication_date 2012/05/09 · arxiv created 2012/06/28 · arxiv updated 2012/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A random chaotic interval map with noise which causes coarse-graining induces a finite-state Markov chain. For a map topologically conjugate to a piecewise-linear map with the Lebesgue measure being ergodic, we prove that the Shannon entropy for the induced Markov chain possesses a finite limit as the noise level tends to zero. In most cases, the limit turns out to be strictly greater than the Lyapunov exponent of the original map without noise.

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