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Abstract: . We present a powerful approach to computing the Hausdorff dimension of certain conformally self-similar sets. We illustrate this method for the dimension dim H (E 2 ) of the set E 2 , consisting of those real numbers whose continued fraction expansions contain only the digits 1 or 2. A very striking feature of this method is that the successive approximations converge to dim(E 2 ) at a super-exponential rate. 0. Introduction Given any number 0 ! x ! 1 we can consider its continued fraction... (Update)
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BibTeX entry: (Update)
@misc{ jenkinson-computing,
author = "O. Jenkinson and M. Pollicott",
title = "Computing The Dimension Of Dynamically Defined Sets I: E2 And
Bounded Continued Fractions.",
url = "citeseer.ist.psu.edu/38470.html" }
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