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In the present work we examine Isaacs' geometric method for the construction of the barrier surface in differential games. We are thus led, in a natural way, to a new (geometric) second-order necessary condition that a valid barrier surface must satisfy. This helps us, on the one hand, to clarify the appearance of a previously discovered qualitatively new type of barrier surface when the problem parameters enter a certain region of the parameter space, and, on the other hand, our systematic anal...
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