Study of probability density for the existence of orbits

点击翻译按钮获取中文摘要

We study some technique for deriving global properties of probability density for the existence of orbits from local conditions on the behaviors of pairwise disjoint orbits. In particular, we show the following result for some dynamical systems: if for every pair of orbits, there exists another orbit which transfers from one orbit to the other, then (1) the probability density for the existence of orbits is uniquely determined, and (2) one can estimate the difference between the probability density for the existence of finite orbit and that of infinite orbit, by using the entropy and the potential.