Geodesic
THE FRACTAL DIMENSION OF INVARIANT SUBSETS FOR PIECEWISE MONOTONIC MAPS ON THE INTERVAL
Acta mathematica Universitatis Comenianae, Tome 64 (1995) no. 2 
F. Hofbauer. THE FRACTAL DIMENSION OF INVARIANT SUBSETS FOR PIECEWISE MONOTONIC MAPS ON THE INTERVAL. Acta mathematica Universitatis Comenianae, Tome 64 (1995) no. 2. http://geodesic.mathdoc.fr/item/AMUC_1995_64_2_a3/
@article{AMUC_1995_64_2_a3,
     author = {F. Hofbauer},
     title = {THE {FRACTAL} {DIMENSION} {OF} {INVARIANT} {SUBSETS} {FOR} {PIECEWISE} {MONOTONIC} {MAPS} {ON} {THE} {INTERVAL}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1995},
     volume = {64},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1995_64_2_a3/}
}
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Voir la notice de l'article provenant de la source Comenius University

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 $A$.