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      Intersections of certain deleted digits sets

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          Abstract

          We consider some properties of the intersection of deleted digits Cantor sets with their translates. We investigate conditions on the set of digits such that, for any t between zero and the dimension of the deleted digits Cantor set itself, the set of translations such that the intersection has Hausdorff dimension equal to t is dense in the set F of translations such that the intersection is non-empty. We make some simple observations regarding properties of the set F, in particular, we characterize when F is an interval, in terms of conditions on the digit set.

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          “Fractals and Self-Similarity,”

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            On existence of subsets of finite measure of sets of infinite measure

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              Intersection of triadic Cantor sets with their translates— I. Fundamental properties

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                Author and article information

                Journal
                17 May 2011
                Article
                10.1142/S0218348X11005518
                1105.3463
                8f1a42b4-13c7-4a89-9d15-38adf2fd9095

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                28A80
                Fractals, Volume: 20, Issue: 1 (March 2012), Page: 105-115
                15 pages, 5 figures
                math.MG

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