Proof of a conjecture of E. Strömgren
Proof of a conjecture of E. Strömgren
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E. Strömgren 猜想的证明
DOI：
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发表时间：
1973
期刊：
影响因子：
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通讯作者：
J. Henrard
中科院分区：
文献类型：
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作者：
J. Henrard
在更一般的两自由度解析哈密顿系统的框架下，讨论了Strömgren猜想，即在限制问题中，一类双渐近轨道是周期轨道族的极限成员。建立了该猜想成为定理的充分条件。这些条件相当于双渐近轨道的横截性条件，并且很可能在文献中所考虑的受限问题的数值探索的情况下得到验证。
The conjecture of Strömgren according to which, in the restricted problem, a class of doubly asymptotic orbits are limit members of families of periodic orbits is examined in the more general framework of analytic Hamiltonian system with two degrees of freedom. Sufficient conditions for the conjecture to become a theorem are established. Theses conditions amount to a transversality condition for the doubly asymptotic orbits and are likely to be verified in the cases considered in the literature of numerical explorations of the restricted problem.