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1 February 2016 2-dimensional badly approximable vectors and Schmidt’s game
Jinpeng An
Duke Math. J. 165(2): 267-284 (1 February 2016). DOI: 10.1215/00127094-3165862

Abstract

We prove that for any pair (s,t) of nonnegative numbers with s+t=1, the set of 2-dimensional (s,t)-badly approximable vectors is winning for Schmidt’s game. As a consequence, we give a direct proof of Schmidt’s conjecture using his game.

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Jinpeng An. "2-dimensional badly approximable vectors and Schmidt’s game." Duke Math. J. 165 (2) 267 - 284, 1 February 2016. https://doi.org/10.1215/00127094-3165862

Information

Received: 16 June 2014; Revised: 30 January 2015; Published: 1 February 2016
First available in Project Euclid: 19 January 2016

zbMATH: 06556668
MathSciNet: MR3457674
Digital Object Identifier: 10.1215/00127094-3165862

Subjects:
Primary: 11J13
Secondary: 11J83 , 11K55 , 11K60

Keywords: badly approximable vector , Schmidt’s game

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 2 • 1 February 2016
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