The Schwarzian Derivative of Iterated Functions

This Demonstration graphs the Schwarzian derivative for iterates of a few different functions of a single variable. Of particular interest in the study of one-dimensional dynamical systems is if a function or some iterate of that function has a Schwarzian derivative that is strictly negative. You can determine if a particular function has this property for some parameter values and by varying the number of iterates taken and examining the graphs of their Schwarzian derivatives.