A Polynomial Time Algorithm for the Hausdorff Dimension of Continued Fraction Cantor Sets

  title={A Polynomial Time Algorithm for the Hausdorff Dimension of Continued Fraction Cantor Sets},
  author={Doug Hensley},
  journal={Journal of Number Theory},
  • D. Hensley
  • Published 1 May 1996
  • Mathematics
  • Journal of Number Theory
For any finite setAof positive integers, letEA :={α∈(0, 1):αis irrational, and every partial quotient in the (infinite) simple continued fraction expansion ofαis an element ofA}. For setsAwith fewer than two elements,EAis uninteresting. For |A|⩾2,EAis a kind of Cantor fractal dust, with a Hausdorff dimension (dim EA) between 0 and 1. This work presents an algorithm which, given a finite setAof between 2 andNpositive integers 2N, determines dim EAto within ±2−NusingO(N7) elementary bit… 
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