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Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval. II. (English) Zbl 0813.28009
Summary: We construct examples of expanding piecewise monotonic maps on the interval which have a closed topologically transitive invariant subset \(A\) with Darboux property, Hausdorff dimension \(d\in (0,1)\) and zero \(d\)- dimensional Hausdorff measure. This shows that the results about Hausdorff and conformal measures proved in the first part of this paper (reviewed above) are in some sense best possible.

MSC:
28D99 Measure-theoretic ergodic theory
54H20 Topological dynamics (MSC2010)
28A78 Hausdorff and packing measures
Citations:
Zbl 0813.28008
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