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<p>In this paper we study the classical Schmidt game on two families of sets: one related to frequencies of digits in base-2 expansions, and one connected to the set of the badly approximable numbers. Namely, we describe some nontrivial winning and losing parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\alpha , \beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for these sets.</p>

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On Nontrivial Winning and Losing Parameters of Schmidt Games

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月14日

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  • Vasiliy Neckrasov,
  • Eric Zhan

摘要

In this paper we study the classical Schmidt game on two families of sets: one related to frequencies of digits in base-2 expansions, and one connected to the set of the badly approximable numbers. Namely, we describe some nontrivial winning and losing parameters \((\alpha , \beta )\) ( α , β ) for these sets.