Hausdorff Dimension and Diophantine Approximation

Details Hausdorff Dimension and Diophantine Approximation Hausdorff Dimension and Diophantine Approximation

2003-05-28

arxiv.org/abs/math/0305399v2

Fractal geometry and applications: a jubilee of Beno\^it Mandelbrot. Part 1, 305--347, Proc. Sympos. Pure Math., 72, Part 1, A

Mathematics

Number Theory

43 pages, 5 figures, to appear in "Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot", Proceedings of Symposia

Scientific paper

We begin with a brief treatment of Hausdorff measure and Hausdorff dimension. We then explain some of the principal results in Diophantine approximation and the Hausdorff dimension of related sets, originating in the pioneering work of Vojtech Jarnik. We conclude with some applications of these results to the metrical structure of exceptional sets associated with some famous problems. It is not intended that all the recent developments be covered but they can be found in the references cited.

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