Phenomenon of narrow throats of level sets of value function in differential games

A number of zero-sum differential games with fixed termination instant are given, in which a level set of the value function has one or more time sections that are almost degenerated (have no interior). Presence of such a peculiarity make very high demands on the accuracy of computational algorithms for constructing value function. Analysis and causes of these degeneration situations are important during study of applied pursuit problems.