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Mat. Teor. Igr Pril., 2017, Volume 9, Issue 2, Pages 105–120 (Mi mgta200)  

Lion and Man game and fixed point free maps

Olga O. Yufereva

Krasovskii Institute of Mathematics and Mechanics

Abstract: This work is related with pursuit-evasion game where Lion is the pursuer and Man is the evader. We suppose that both players move in a metric space, have equal maximum speeds and complete information about the location of each other. We say that Man wins if he can escape a capture with non-zero radius; more precisely if there exists a positive number p and a non-anticipative strategy for some players' initial positions, that let him always be out of Lion's p-neighbourhood. We study sufficient conditions of the existence of Man's winning strategy. In this way we use the metric properties of space (mainly geodesics' behavior and fixed-point free maps). The technique requires neither convexity nor finite dimension of a space.

Keywords: pursuit-evasion game, lion and man game, fixed point, geodesic loop.

Funding Agency Grant Number
Russian Science Foundation 17-11-01093


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English version:
Automation and Remote Control, 2018, 79:7, 1361–1370

Bibliographic databases:

UDC: 517.977
BBK: 22.16

Citation: Olga O. Yufereva, “Lion and Man game and fixed point free maps”, Mat. Teor. Igr Pril., 9:2 (2017), 105–120; Autom. Remote Control, 79:7 (2018), 1361–1370

Citation in format AMSBIB
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\by Olga~O.~Yufereva
\paper Lion and Man game and fixed point free maps
\jour Mat. Teor. Igr Pril.
\yr 2017
\vol 9
\issue 2
\pages 105--120
\mathnet{http://mi.mathnet.ru/mgta200}
\transl
\jour Autom. Remote Control
\yr 2018
\vol 79
\issue 7
\pages 1361--1370
\crossref{https://doi.org/10.1134/S0005117918070135}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438654700013}


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