  The mathematical model proposed by George Soros for his theory of reflexivity
is analyzed under the framework of discrete dynamical systems. We show the
importance of the notion of fixed points for explaining the behavior of a
reflexive system governed by its cognitive and manipulative functions. The
interrelationship between these two functions induces fixed points with
different characteristics, which in turn generate various system behaviors
including the so-called "boom then bust" phenomenon in Soros's theory.
