在哪里放置一个洞，以实现最大的逃生率
Where to place a hole to achieve a maximal escape rate
摘要：
一个很自然的问题，即生存概率如何取决于一个洞的位置，似乎从来没有在开放的动力系统理论中得到解决。我们发现这种依赖可能是非常重要的。主要结果与强混沌映射的相空间中的等尺寸（测度）空洞有关。在每个孔中取一个最小周期的周期点。然后，通过该最小周期呈现其最大值的孔发生更快的逃逸。结果是有效的所有有限的时间（从最小周期），这是不寻常的动力系统理论，其中通常陈述是渐近时，时间趋于无穷大。很明显，洞越大，通过这个洞的逃逸就越大。我们的研究结果表明，一般来说，这是不正确的，和特定功能的动态可能会发挥作用的大小相媲美的洞。
英文摘要：
A natural question of how the survival probability depends upon a position of a hole was seemingly never addressed in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related to the holes with equal sizes (measure) in the phase space of strongly chaotic maps. Take in each hole a periodic point of minimal period. Then the faster escape occurs through the hole where this minimal period assumes its maximal value. The results are valid for all finite times (starting with the minimal period) which is unusual in dynamical systems theory where typically statements are asymptotic when time tends to infinity. It seems obvious that the bigger the hole is the bigger is the escape through that hole. Our results demonstrate that generally it is not true, and that specific features of the dynamics may play a role comparable to the size of the hole.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
