论文标题
不可综合系统的定量行为（III）
Quantitative behavior of non-integrable systems (III)
论文作者
论文摘要
部分（III）的主要目的是在polysquares中给出明确的大地测量和台球轨道，这些轨道表现出时间定量密度。在许多情况下，我们甚至可以建立一种称为超级密度的最佳时间形式。我们还研究了无限的平坦动力学系统，包括周期性的和上的静态系统，其中包括无限多质量区域的台球。特别是，即使对于上的系统，我们也可以证明时间量化密度。在光学方面，台球情况相当于结果，即显式的单射线可以从本质上照亮整个无限的多质量区域，而边界充当镜子。实际上，我们表明，相同的初始方向可以适用于此类无限系统的不可数家庭。
The main purpose of part (III) is to give explicit geodesics and billiard orbits in polysquares that exhibit time-quantitative density. In many instances, we can even establish a best possible form of time-quantitative density called superdensity. We also study infinite flat dynamical systems, both periodic and aperiodic, which include billiards in infinite polysquare regions. In particular, we can prove time-quantitative density even for aperiodic systems. In terms of optics the billiard case is equivalent to the result that an explicit single ray of light can essentially illuminate a whole infinite polysquare region with reflecting boundary acting as mirrors. In fact, we show that the same initial direction can work for an uncountable family of such infinite systems.
