On Limit- and Infimum-Captures in Pursuit-Evasion Problems ?

摘要

In this paper, we show an example of two-person pursuit-evasion game with infinite horizon where two kinds of capture turn out to differ. One of them, the infimum capture, is a standard kind of capture, while the limit capture, introduced in this paper, is its stronger variant. Both variants of capture have applications, but it is not known in advance whether they always exist simultaneously. The considered example is based on Lion and Man game, i.e. on the game with equal players’ capabilities. The considered space is a compact geodesic space.