标题： n中心台球的不可积性 显示英文标题

标题： Non-integrability of n-centre billiards

摘要： 我们研究一类机械弹道，其中粒子在平面区域内受n中心势的影响，并在直墙上发生弹性反射。 受玻尔兹曼原始弹道模型的启发，我们探讨此类系统何时不具有可积性。 我们证明，对于任何正能，如果至少有两个中心，并且墙放置得足够远，那么弹道动力学必然不可积并表现出混沌行为。 在经典的牛顿二中心问题中，我们确定了关于墙的一个简单几何条件，同样保证混沌，尽管自由二中心系统是可积的。 显示英文摘要

摘要： We investigate a class of mechanical billiards, where a particle moves in a planar region under the influence of an n-centre potential and reflects elastically on a straight wall. Motivated by Boltzmann's original billiard model we explore when such systems fail to be integrable. We show that for any positive energy, if there are at least two centres and the wall is placed sufficiently far away, the billiard dynamics is necessarily non-integrable and exhibits chaotic behaviour. In the classical Newtonian two-centre problem, we identify a simple geometric condition on the wall that likewise guarantees chaos, even though the free two-centre system is integrable.