THE FRACTAL DIMENSION OF INVARIANT SUBSETS FOR PIECEWISE MONOTONIC MAPS ON THE INTERVAL
F. HOFBAUER
Abstract.
We consider completely invariant subsets $A$ of weakly expanding piecewise monotonic transformations $T$ on $[0,1]$. It is shown that the upper box dimension of $A$ is bounded by the minimum $t_A$ of all parameters $t$ for which a $t$-conformal measure with support $A$ exists. In particular, this implies equality of box dimension and Hausdorff dimension of $A$.
Compressed Postscript 
