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- W1569969683 abstract "We introduce and develop a class of textit{Cantor-winning} sets that share the same amenable properties as the classical winning sets associated to Schmidt's $(alpha,beta)$-game: these include maximal Hausdorff dimension, invariance under countable intersections with other Cantor-winning sets and invariance under bi-Lipschitz homeomorphisms. It is then demonstrated that a wide variety of badly approximable sets appearing naturally in the theory of Diophantine approximation fit nicely into our framework. As applications of this phenomenon we answer several previously open questions, including some related to the Mixed Littlewood conjecture and the $times2, times3$ problem." @default.
- W1569969683 created "2016-06-24" @default.
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- W1569969683 date "2015-03-16" @default.
- W1569969683 modified "2023-09-27" @default.
- W1569969683 title "Cantor-winning sets and their applications" @default.
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