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

abstract

• For any finite set A of positive integers, let EA := { (0, 1): is irrational, and every partial quotient in the (infinite) simple continued fraction expansion of is an element of A}. For sets A with fewer than two elements, EA is uninteresting. For A2, EA is 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 set A of between 2 and N positive integers 2N, determines dim EA to within 2-N using O(N7) elementary bit operations. There is also a convenient implementation of the algorithm in Mathematica code, together with a small table and some conjectures. 1996 Academic Press, Inc.

authors

• Hensley, Douglas

published proceedings

• Journal of Number Theory

altmetric score

• 3

author list (cited authors)

• Hensley, D.

citation count

• 49

complete list of authors

• Hensley, Douglas

publication date

• May 1996

publisher

• Elsevier  Publisher

published in

• Journal of Number Theory  Journal

Digital Object Identifier (DOI)

• 10.1006/jnth.1996.0058

start page

• 9

end page

• 45

volume

• 58

issue

• 1

URL

• http://dx.doi.org/10.1006/jnth.1996.0058