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Hausdorff–Lebesgue Dimension of Attractors
Preview AbstractDefinitions of Hausdorff–Lebesgue measure and dimension are introduced. Combination of Hausdorff and Lebesgue ideas are used. Methods for upper and lower estimations of attractor dimensions are developed.
INTERSECTIONS OF CERTAIN DELETED DIGITS SETS
Preview AbstractWe 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.