  We study the topological entropy of a two-parameter family of maps related to
(a,b)-continued fraction algorithms and prove that it is constant on a square
within the parameter space (two vertices of this square correspond to
well-studied continued fraction algorithms). The proof uses conjugation to maps
of constant slope. We also present experimental evidence that the topological
entropy is flexible (i.e., takes any value in a range) on the whole parameter
space.

Dynamical Systems