The Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game
Lior Fishman, Vanessa Reams, David Simmons
TL;DR
This paper introduces two new mathematical games that merge existing concepts and explores their properties and applications to Diophantine approximation, revealing insights into the geometric structure of related sets.
Contribution
The paper presents the first formulation and analysis of the Banach-Mazur-Schmidt and Banach-Mazur-McMullen games, connecting game theory with Diophantine approximation.
Findings
New games exhibit unique strategic properties
Application to Diophantine approximation enhances understanding of set structures
Provides a framework linking geometric and number-theoretic concepts
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Holomorphic and Operator Theory · Point processes and geometric inequalities