ON THE CONSTRUCTION OF ONE-DIMENSIONAL ITERATIVE MAPS FROM THE INVARIANT DENSITY - THE DYNAMICAL ROUTE TO THE BETA-DISTRIBUTION

Using the Frobenius-Perron functional equation we construct a one-dime nsional iterative map resulting from a given invariant density. As a s pecific example we focus on the symmetric beta distribution and obtain a class of maps with a broad range of universal properties. The analy tical behaviour as well as the bifurcation routes of these maps are st udied in some detail.