A note on Farey sequences and Hausdorff dimension

Details A note on Farey sequences and Hausdorff dimension A note on Farey sequences and Hausdorff dimension

1999-02-15

arxiv.org/abs/math-ph/9902018v1

Physics

Mathematical Physics

4 pages, latex

Scientific paper

We prove that the Farey sequences can be express into equivalence classes
labeled by a fractal parameter which looks like a Hausdorff dimension $h$
defined within the interval 1 < h < 2. The classes $h$ satisfy the same
properties of the Farey series and for each value of $h$ there exists an
algebraic equation.

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