On the mixing coefficients of piecewise monotonic maps

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 β-transformations, non-φ-mixing is generic. In this sense, the asymmetry of φ-mixing is natural.