The Banach-Mazur-Schmidt and Banach-Mazur-McMullen games

Lior Fishman; Vanessa Reams; David Simmons

doi:10.1016/j.jnt.2016.03.021

The Banach-Mazur-Schmidt and Banach-Mazur-McMullen games

Lior Fishman, Vanessa Reams, David Simmons

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce two new mathematical games, the Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game, merging well-known games. We investigate the properties of the games, as well as providing an application to Diophantine approximation theory, analyzing the geometric structure of certain Diophantine sets.

Original language	English
Pages (from-to)	169-179
Number of pages	11
Journal	Journal of Number Theory
Volume	167
DOIs	https://doi.org/10.1016/j.jnt.2016.03.021
State	Published - 1 Oct 2016
Externally published	Yes

Keywords

Banach-Mazur game
Diophantine approximation
Schmidt's game

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2016.03.021

Cite this

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abstract = "We introduce two new mathematical games, the Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game, merging well-known games. We investigate the properties of the games, as well as providing an application to Diophantine approximation theory, analyzing the geometric structure of certain Diophantine sets.",

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AB - We introduce two new mathematical games, the Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game, merging well-known games. We investigate the properties of the games, as well as providing an application to Diophantine approximation theory, analyzing the geometric structure of certain Diophantine sets.

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The Banach-Mazur-Schmidt and Banach-Mazur-McMullen games

Abstract

Keywords

ASJC Scopus subject areas

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