On solving a pursuit game problem with fixed termination time

A pursuit game problem for the first player with fixed termination time is considered. An approximate method is suggested for constructing the positional absorption set, which is the solvability set for the pursuit problem. Recurrence relations are written that define a system of sets approximating the positional absorption set in the phase space of the conflict-controlled system. A resolving control procedure with a guide is described, which copies the controls.