On the mixing coefficients of piecewise monotonic maps

Abstract

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

correction of misprint in the definition of weak mixing