On Families of Periodic Orbits in the Restricted Three-Body Problem

被引：0
作者：
Seongchan Kim
机构：
[1] Universität Augsburg,
来源：
Qualitative Theory of Dynamical Systems | 2019年 / 18卷
关键词：
The restricted three-body problem; Families of periodic orbits; Arnold’s ; -invariant; Stark–Zeeman system;
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摘要：
Since Poincaré, periodic orbits have been one of the most important objects in dynamical systems. However, searching them is in general quite difficult. A common way to find them is to construct families of periodic orbits which start at obvious periodic orbits. On the other hand, given two periodic orbits one might ask if they are connected by an orbit cylinder, i.e., by a one-parameter family of periodic orbits. In this article we study this question for a certain class of periodic orbits in the planar circular restricted three-body problem. Our strategy is to compare the Cieliebak–Frauenfelder–van Koert invariants which are obstructions to the existence of an orbit cylinder.
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页码：201 / 232
页数：31
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