Invariant measures of piecewise fractional linear maps and piecewise quadratic maps

Abstract

In this paper, we first extend the main result of the paper “Differentiable equivalence of fractional linear maps” to maps with more than three branches and in the second part we comment and correct some results on so-called exceptional dual systems. Here we also give some connections to so-called flipped maps. The third part is devoted to piecewise quadratic maps. The most interesting case seems to be Bolyai’s algorithm which was brought back to the mathematical audience by A. Rényi.