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On the mixing coefficients of piecewise monotonic maps

Jon Aaronson·Hitoshi Nakada
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Abstract

We investigate the mixing coefficients of interval maps satisfying Rychlik's conditions. A mixing Lasota-Yorke map is reverse $ϕ$-mixing. If its invariant density is uniformly bounded away from 0, it is $ϕ$-mixing iff all images of all orders are big in which case it is $ψ$-mixing. Among $\b$-transformations, non-$ϕ$-mixing is generic. In this sense, the asymmetry of $ϕ$-mixing is natural.

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Jon Aaronson, Hitoshi Nakada. 2006-11-09. On the mixing coefficients of piecewise monotonic maps. https://arxiv.org/abs/math/0408205

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