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Abstract
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We analyze, based on an interplay between ideas and techniques from logic and
geometric analysis, a pursuit-evasion game. More precisely, we focus on a uniform
betweenness property and use it in the study of a discrete lion and man game with an
-capture
criterion. In particular, we prove that in uniformly convex bounded domains the lion
always wins and, using ideas stemming from proof mining, we extract a uniform rate
of convergence for the successive distances between the lion and the man. As a
byproduct of our analysis, we study the relation among different convexity properties
in the setting of geodesic spaces.
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Keywords
lion and man game, rate of convergence, uniform convexity,
betweenness property
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Mathematical Subject Classification 2010
Primary: 49N75, 91A24
Secondary: 03F10, 53C23
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Milestones
Received: 8 August 2019
Revised: 18 May 2020
Accepted: 6 June 2020
Published: 26 January 2021
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