Dimensionfor Invariant Subsets of Interval Mapsp
نویسنده
چکیده
Let T : 0;1] ! 0;1] be an expanding piecewise monotonic map, and consider the set R of all points, whose orbits omit a certain nite union of open intervals. It is shown that the Hausdorr dimension HD (R) depends continuously on small perturbations of the endpoints of these open intervals. A similar result for the topological pressure is also obtained. Furthermore it is shown that for every t 2 0;1] there exists a closed, T-invariant Rt 0;1] with HD (Rt) = t. Finally it is proved that the Hausdorr dimension of the set of all points, whose orbit is not dense, is 1.
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