Hamilton流中的直线轨道
Straight Line Orbits in Hamiltonian Flows
摘要：
我们研究周期性的直线轨道（SLO）在哈密顿力场使用直接和逆方法。本文证明了任意维动量平方的自然哈密顿量的一个普遍定理，并将其推广到二维和三维。接下来，我们专门讨论齐次势及其叠加，包括熟悉的Hénon-Heiles问题。证明了对于$N$ -形式的任意有限叠加，SLO可以存在.结果被应用到一个家庭的广义Hénon-Heiles潜在的离散旋转对称。SLO的也被发现这些潜力的叠加。
英文摘要：
We investigate periodic straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta in arbitrary dimension and specialized to two and three dimension. Next we specialize to homogeneous potentials and their superpositions, including the familiar Hénon-Heiles problem. It is shown that SLO's can exist for arbitrary finite superpositions of $N$-forms. The results are applied to a family of generalized Hénon-Heiles potentials having discrete rotational symmetry. SLO's are also found for superpositions of these potentials.
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