Nowhere coexpanding functions

We establish results on the number and nature of the fixed points of these functions, including a generalisation of a classic result of Singer. Lead paragraph The set of functions with negative Schwarzian derivative is closed under composition. As a result, it is a popular tool for studying the dynamics of functions in dimension one. A comprehensive treatment involving one-dimensional dynamics, with many results involving negative Schwarzian derivatives, is given in the book of de Melo and van Strien [1993].