The Fractal Dimension of Invariant Subsets for Piecewise Monotonic Maps on the Interval
نویسنده
چکیده
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 tA 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.
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Continuity of the Hausdorff Dimension for Invariant Subsets of Interval Maps
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