A natural question of how the survival probability depends upon a position ofa hole was seemingly never addressed in the theory of open dynamical systems.We found that this dependency could be very essential. The main results arerelated to the holes with equal sizes (measure) in the phase space of stronglychaotic maps. Take in each hole a periodic point of minimal period. Then thefaster escape occurs through the hole where this minimal period assumes itsmaximal value. The results are valid for all finite times (starting with theminimal period) which is unusual in dynamical systems theory where typicallystatements are asymptotic when time tends to infinity. It seems obvious thatthe bigger the hole is the bigger is the escape through that hole. Our resultsdemonstrate that generally it is not true, and that specific features of thedynamics may play a role comparable to the size of the hole.
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