Fractal properties of invariant subsets for piecewise monotonic maps on the interval

Hofbauer, Franz; Urbański, Mariusz

doi:10.1090/S0002-9947-1994-1232188-9

Fractal properties of invariant subsets for piecewise monotonic maps on the interval
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by Franz Hofbauer and Mariusz Urbański PDF

Trans. Amer. Math. Soc. 343 (1994), 659-673 Request permission

Abstract:

Let T be a piecewise monotonic transformation on [0, 1] 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.

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