Abstract
Strongly chaotic systems (e.g., piecewise expanding mappings) exhibit diffusion-like behavior in the sense of central limit theorems. To find more precise statements about the similarity to probabilistic diffusion, we study how the evolution of probability densities underd-dimensional piecewise expanding mappings can be modeled by Markov processes with smooth transition probabilities (such as diffusion processes). Our results can be viewed as a special type of local limit theorem.
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Loviscach, J. Probabilistic models of multidimensional piecewise expanding mappings. J Stat Phys 75, 189–213 (1994). https://doi.org/10.1007/BF02186286
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DOI: https://doi.org/10.1007/BF02186286