A Family of Eventually Expanding Piecewise Linear Maps of the Interval

Abstract We show that for every 0 < s ≤ 1 < p the piecewise linear map fs,p on the interval [0, 1] given by an expanding branch px for 0 ≤ x ≤ 1/p, and a contracting branch sx − s/p for 1/p < x ≤ 1, is eventually piecewise expanding and exact.