论文标题
双曲线多边形台球的桥梁
Bridge to Hyperbolic Polygonal Billiards
论文作者
论文摘要
众所周知，多边形的台球不能混乱（双曲线）。任何多边形台球的kolmogorov-sinai熵均为零。我们考虑物理多边形的台球，其中移动粒子是硬盘而不是点（数学）粒子，并表明典型的物理多边形台球至少在积极度量的子集中是双曲线，因此，kolmogorov-sinai熵的kolmogorov-sinai熵是动态粒子的任何积极半径（前提是粒子都不是如此之大，以至于它不能移动到多头性粒子内）。之所以发生这种情况，是因为典型的物理多边形台球等于数学（点粒子）半分散台球。我们还猜想，实际上多边形的典型物理台球在相同的条件下是颈。
It is well-known that billiards in polygons cannot be chaotic (hyperbolic). Particularly Kolmogorov-Sinai entropy of any polygonal billiard is zero. We consider physical polygonal billiards where a moving particle is a hard disc rather than a point (mathematical) particle and show that typical physical polygonal billiard is hyperbolic at least on a subset of positive measure and therefore has a positive Kolmogorov- Sinai entropy for any positive radius of the moving particle (provided that the particle is not so big that it cannot move within a polygon). This happens because a typical physical polygonal billiard is equivalent to a mathematical (point particle) semi-dispersing billiard. We also conjecture that in fact typical physical billiard in polygon is ergodic under the same conditions.
