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THE HAUSDORFF DIMENSION OF SOME PLANAR SETS WITH UNBOUNDED DIGITS

Nakajima, Yuto 大阪大学 DOI:10.18910/89328

2022.10

概要

We consider some parameterized planar sets with unbounded digits. We investigate these sets by using the method of “transversality”, which is the main tool in investigating self-similar sets with overlaps. We calculate the Hausdorff dimension of these sets for typical parameters in some region with respect to the 2-dimensional Lebesgue measure. In addition, we estimate the local dimension of the exceptional set of parameters.

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