Bounding the Dimension of Points on a Line
Lecture Notes in Computer Science(2020)
摘要
We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff dimension of the point \((x,ax+b)\), given real numbers a, b, and x. We apply our main theorem to a problem in fractal geometry, giving an improved lower bound on the (classical) Hausdorff dimension of generalized sets of Furstenberg type.
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关键词
Effective dimension,Kolmogorov complexity,Fractal geometry
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