A Differential Game with Two Players and One Target

We study a two-player differential game in which one of the players wants the state of the system to reach an open target, while the other player wants the state of the system to avoid this target. We show that the victory domains of the players form a partition of the complement of the target. One of them can be characterized by the mean of geometrical conditions (as a "discriminating domain"). Finally we show that the common boundary of the victory domains enjoys a semipermeability property.