On the mixing coefficients of piecewise monotonic maps

Details On the mixing coefficients of piecewise monotonic maps On the mixing coefficients of piecewise monotonic maps

2004-08-16

arxiv.org/abs/math/0408205v4

as in: Probability in mathematics. Israel J. Math. 148 (2005), 1--10

Mathematics

Dynamical Systems

correction of misprint in the definition of weak mixing

Scientific paper

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

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