Almost no points on a Cantor set are very well approximable

By Barak Weiss. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2001

66 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/210e83b67807794469796b23bd480a24dd98960d

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Citations in the corpus

On a problem of K. Mahler: Diophantine approximation and Cantor sets (2005, background): “The Cantor set K together with the Cantor measure μ fall into this general theory – see [11, 15, 17].”
Diophantine approximation and Cantor sets (2008, background): “Even the extension of Weiss’ result [17] is not known; see Kristensen [9] for partial results.”
Badly approximable vectors on fractals (2005, methodology): “Fix a Euclidean structure on Rn+1, and for g 2 G and V 2 W dene ‘V (g) to be the covolume of gV \ gZn+1 in gV . Equivalently, one can extend the Euclidean norm k k from Rn+1 to its exterior algebra, and”
Metric Diophantine approximation: The Khintchine--Groshev theorem for non-degenerate manifolds (2002, background): “The latter can be supported on fractal subsets of R (see [ Wei01 ]) or Rn ([KLW02],”
The set of badly approximable vectors is strongly C1 incompressible (2011, result): “Games played on proper subsets An application of Schmidt games to proving abundance of badly approximable vectors on certain fractal subsets of R first appeared in [12], and was motivated by earlier related results [33, 17, 18, 21].”
On fractal measures and diophantine approximation (2005, background): “In [ W1 ], the third-named author treated the one-dimensional case, and showed that any measure ¹ on R satisfying a certain geometric decay condition introduced by W. Veech [V] (for example, the Hausdorff measure on the standard Cantor ternary set) is extremal (which in the one-dimensional case is e”