论文标题
随机轨道之间的最小距离
Minimal distance between random orbits
论文作者
论文摘要
我们研究了具有足够好的混合特性的随机动力学系统中两个长度N的两个轨道段之间的最小距离。这个问题已经在非随机动力学系统中解决，平均在随机动力学系统（所谓的退火版本中）：众所周知，这个问题的渐近行为由与不变的度量相关的尺寸样量化给出，称为其相关维度（或r {é} nyi} nyi entropy）。我们研究了类似的淬火问题，并表明渐近行为更多地涉及：显示两个相关维度，从而导致相关渐近指数的非平滑行为。
We study the minimal distance between two orbit segments of length n, in a random dynamical system with sufficiently good mixing properties. This problem has already been solved in non-random dynamical system, and on average in random dynamical systems (the so-called annealed version of the problem): it is known that the asymptotic behavior for this question is given by a dimension-like quantity associated to the invariant measure, called its correlation dimension (or R{é}nyi entropy). We study the analogous quenched question, and show that the asymptotic behavior is more involved: two correlation dimensions show up, giving rise to a non-smooth behavior of the associated asymptotic exponent.
