  In this paper we construct a correspondence between the parameter spaces of
two families of one-dimensional dynamical systems, the alpha-continued fraction
transformations T_alpha and unimodal maps. This correspondence identifies
bifurcation parameters in the two families, and allows one to transfer
topological and metric properties from one setting to the other. As an
application, we recover results about the real slice of the Mandelbrot set, and
the set of univoque numbers.
