Lion and Man Game and Fixed Point-Free Maps
Olga Yufereva · Automation and Remote Control · 2018
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.