ON THE MIXING PROPERTIES OF PIECEWISE EXPANDING MAPS UNDER COMPOSITION WITH PERMUTATIONS, II: MAPS OF NON-CONSTANT ORIENTATION

For an integer m ≥ 2, let 𝒫m be the partition of the unit interval I into m equal subintervals, and let ℱm be the class of piecewise linear maps on I with constant slope ±m on each element of 𝒫m. We investigate the effect on mixing properties when f ∈ℱm is composed with the interval exchange map given by a permutation σ ∈ SN interchanging the N subintervals of 𝒫N. This extends the work in a previous paper [N. P. Byott, M. Holland and Y. Zhang, DCDS 33 (2013) 3365–3390], where we considered only the “stretch-and-fold” map fsf(x) = mx mod 1.

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