INTERSECTIONS OF CERTAIN DELETED DIGITS SETS
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 that 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.
2019 ◽
Vol 2019
(746)
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pp. 149-170
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1965 ◽
Vol 61
(3)
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pp. 679-694
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2000 ◽
Vol 43
(3)
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pp. 330-342
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Keyword(s):
ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE
2004 ◽
Vol 04
(01)
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pp. 63-76
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2013 ◽
Vol 56
(2)
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pp. 292-305
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1985 ◽
Vol 5
(1)
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pp. 27-46
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1995 ◽
Vol 06
(01)
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pp. 19-32
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