标题： $N$体系统的 McMillan 映射的推广 显示英文标题

标题： Generalizations of the McMillan map to $N$-body systems

摘要： McMillan映射是一个著名的例子，它是一个在二维相空间中单粒子的有理可积系统。 一篇最近发表的优雅论文将McMillan映射推广到$N$体系统，其中粒子在$d$空间维度中运动。 本文提出了McMillan映射到$N$体系统的某些替代推广（也是完全可积的）。 在所有情况下，相空间都被动力变量中的双二次曲线（以及一组适当选择的角动量变量）所分层。 还证明了将McMillan映射推广到$N$体系统的约束并不是微不足道的。 显示英文摘要

摘要： The McMillan map is a well-known example of a rational integrable system for one particle in a two-dimensional phase space. An elegant recent paper presented a generalization of the McMillan map to an $N$-body system, for particles moving in $d$ space dimensions. This paper presents some alternative generalizations (also completely integrable) of the McMillan map to $N$-body systems. In all cases, the phase space is foliated by a biquadratic curve in the dynamical variables (and a set of suitably chosen angular momentum variables). It is also demonstrated that the constraints to generalize the McMillan map to $N$-body systems are not trivial.