标题： 庞加莱逆问题与相空间中的环面构造 显示英文标题

标题： Poincaré inverse problem and torus construction in phase space

摘要： 可积哈密顿系统的相空间由不变环面组成。 对于任意哈密顿量 H，这样的叶状结构可能不存在，但我们可以通过参数化的曲面族人为构造一个，目的是在某种意义上找到最接近 H 的可积近似。 这就是庞加莱逆问题（PIP）。 在本文中，我们回顾了解决 PIP 的现有方法，并提出一种新的迭代方法，该方法在处理常有问题的薄轨道时效果良好。 显示英文摘要

摘要： The phase space of an integrable Hamiltonian system is foliated by invariant tori. For an arbitrary Hamiltonian H such a foliation may not exist, but we can artificially construct one through a parameterised family of surfaces, with the intention of finding, in some sense, the closest integrable approximation to H. This is the Poincar\'e inverse problem (PIP). In this paper, we review the available methods of solving the PIP and present a new iterative approach which works well for the often problematic thin orbits.