Hyperbolicity of the invariant set for the logistic map with mu > 4

Classic results due to Guckenheimer and Misiurewicz imply that the invarian t set of the logistic map with mu is an element of (4,2 + root5] is hyperbo lic. This is well known, but the only obvious reference in the literature u ses relatively sophisticated ideas from complex variable theory. This pedag ogical note provides a brief, self-contained account of this result using o nly elementary real analysis. The method also gives a good estimate of the expansion rate on the invariant set.