Multifractal dimensions for invariant subsets of piecewise monotonic interval maps
نویسندگان
چکیده
منابع مشابه
The Fractal Dimension of Invariant Subsets for Piecewise Monotonic Maps on the Interval
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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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 ...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2003
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm176-3-2