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Computing the Dimension of Dynamically Defined Sets: E_2 and Bounded Continued Fractions  (Make Corrections)  
Oliver Jenkinson, Mark Pollicott



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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 H (E 2 ) at a super-exponential rate. 0. Introduction Given any number 0 ! x ! 1 we can consider its continued... (Update)

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BibTeX entry:   (Update)

@misc{ jenkinson-computing,
  author = "Oliver Jenkinson and Mark Pollicott",
  title = "Computing the Dimension of Dynamically Defined Sets: E_2 and Bounded Continued
    Fractions",
  url = "citeseer.ist.psu.edu/413406.html" }
Citations (may not include all citations):
439   An Introduction to the Theory of Numbers (context) - Hardy, Wright - 1979
83   Zeta functions and the periodic orbit structure of hyperboli.. (context) - Parry, Pollicott - 1990
40   Mathematical foundations and applications (context) - Falconer, geometry - 1990
37   Repellers for real analytic maps (context) - Ruelle - 1982
28   Produits tensoriels topologiques et espaces nucl'eaires (context) - Grothendieck - 1955
25   Zeta functions for expanding maps and Anosov flows (context) - Ruelle - 1976
22   Methods of modern mathematical physics vol (context) - Reed, Simon - 1980
19   Hausdorff dimension of quasicircles (context) - Bowen - 1979
17   Recycling of strange sets (context) - Artuso, Aurell et al. - 1990
11   Hausdorff dimension for horseshoes (context) - McCluskey, Manning - 1983
7   The Laplacian for domains in hyperbolic space and limit sets.. (context) - Phillips, Sarnak
5   Uber die Approximation irrationaler Zahlen durch rationale I.. (context) - Perron - 1921
5   The Hausdorff dimensions of some continued fraction Cantor s.. (context) - Hensley - 1989
5   Continuants with bounded digits (context) - Cusick - 1977
4   Symbolic dynamics and Hyperbolic spaces (context) - Mayer, fractions et al. - 1991

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