Automation and Remote Control

, Volume 79, Issue 7, pp 1361–1370 | Cite as

Lion and Man Game and Fixed Point-Free Maps

  • O. O. YuferevaEmail author
Mathematical Game Theory and Applications


This paper is dedicated to the pursuit-evasion game in which both players (Lion and Man) move in a metric space, have equal maximum speeds and complete information about the location of each other. We assume that evasion is successful if, for some initial positions of players, there exists a positive number p and an evader’s non-anticipative strategy guaranteeing that the distance between the players is always greater than p. We consider connection between successful evasion and such properties of the phase space as geodesics behavior and the existence of non-expanding fixed point-free self-maps.


pursuit-evasion game lion and man fixed points geodesic loop 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and MechanicsYekaterinburgRussia

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