FRACTAL PROPERTIES OF INVARIANT SUBSETS FOR PIECEWISE MONOTONIC MAPS ON THE INTERVAL

Let T be a piecewise monotonic transformation on [0, I] and let A be a T-invariant subset, which has positive topological entropy and satisfies the Darboux property. A general existence theorem for conformal measures on A is proved. This is then used to show equality of the dynamical dimension of A and the minimal zero of a certain pressure function.