The lion and man problem - revisited (Q1060979)

A pursuer P, whose speed is bounded by 1, wants to get closer to an evader E, whose speed is bounded by \(\omega >1\). P wants to reduce his distance PE from E below the capture radius \(\rho\). Both players are confined to a circular arena. This problem is equivalent to a problem discussed by \textit{J. Flynn} [SIAM J. Control 12, 581-597 (1974; Zbl 0289.90047)], who characterized and gave numerical bounds to the least upper bound \(d^*\) on the values of PE that E can maintain. He used direct methods and did not use Isaacs' theory. We solve our problem relying on the theory of singular surfaces in differential games. We construct and investigate barriers of the game of kind, and we replace Flynn's bounds on \(d^*\) by analytical (exact) values for various speeds \(\omega\).