We define two functions f and g on the unit interval [0, 1] to be strongly conjugate $\operatorname {iff}$ there is an order-preserving homeomorphism h of [0, 1] such that g = h -1 fh (a minor ...

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 ...