On conjugacies between asymmetric Bernoulli shifts

This paper investigates conjugacies between asymmetric Bernoulli shifts. It is shown that there exist a unique increasing conjugacy and a unique decreasing conjugacy. We respectively construct a sequence of functions to approximate these two conjugacies, and give an estimation for the error of the approximation. We also present explicit formulae of these two conjugacies. It is shown that these two conjugacies are singular, Hölder continuous and not differentiable.