|
%I #20 Jul 13 2023 01:06:42
%S 5,3,1,2,8,0,5,0,6,2,7,7,2,0,5,1,4,1,6,2,4,4,6,8,6,4,7,3,6,8,4,7,1,7,
%T 8,5,4,9,3,0,5,9,1,0,9,0,1,8,3,9,8,7,7,9,8,8,8,3,9,7,8,0,3,9,2,7,5,2,
%U 9,5,3,5,6,4,3,8,3,1,3,4,5,9,1,8,1,0,9,5,7,0,1,8,1,1,8,5,2,3,9,8
%N Decimal expansion of Hausdorff dimension of E_{1,2}: set of irrationals whose continued fraction expansion consists only of 1's and 2's.
%H Andrey Zabolotskiy, <a href="/A279903/b279903.txt">Table of n, a(n) for n = 0..199</a> (from Pollicott & Vytnova)
%H Oliver Jenkinson, <a href="http://dx.doi.org/10.1142/S0219493704000900">On the density of Hausdorff dimensions of bounded type continued fraction sets: The Texan conjecture</a>, Stoch. Dyn. 04, 63 (2004).
%H Oliver Jenkinson and Mark Pollicott, <a href="https://arxiv.org/abs/1611.09276">Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets: a hundred decimal digits for the dimension of E_2</a>, arXiv:1611.09276 [math.DS], 2016.
%H M. H. Kolkhuis Tanke, <a href="https://www.universiteitleiden.nl/binaries/content/assets/science/mi/scripties/kolkhuis_tanke.pdf">Continued fractions with restricted digits and their Hausdorff dimension</a> (bachelor thesis), 2016.
%H M. Pollicott and P. Vytnova, <a href="https://doi.org/10.1090/btran/109">Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups</a>, Trans. Amer. Math. Soc. Ser. B, 9 (2022), 1102-1159.
%H J. Thurlby, <a href="https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.840285">Rigorous calculations of renormalisation fixed points and attractors</a>, PhD thesis, U. Portsmouth, (2021), eq. (5.42)
%e dim(E_{1,2}) = 0.531280506277205141624468647368471785493059109018398779...
%K nonn,cons
%O 0,1
%A _Andrey Zabolotskiy_, Dec 22 2016
%E More terms from _Andrey Zabolotskiy_, Aug 08 2017 from Jenkinson & Pollicott, 2016.
|
