Stability diagram for 4D linear periodic systems with applications to homographic solutions
Stability diagram for 4D linear periodic systems with applications to homographic solutions
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DOI：
10.1016/j.jde.2006.01.014
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发表时间：
2006-07
影响因子：
2.4
通讯作者：
R. Martínez;Anna Samà;C. Simó
中科院分区：
文献类型：
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作者：
R. Martínez;Anna Samà;C. Simó
本文考虑一类4维Hamilton时间周期线性系统，它依赖于三个参数λ1，λ 2和ε，使得当ε=0时系统成为自治的.利用规范形技术研究了ε>0足够小时的稳定性和分支。我们特别关注达朗贝尔案。结果被应用于研究平面三体问题单应解的线性稳定性，对于某些−α次齐次势，0 <α<2，包括牛顿情形。
We consider a family of 4-dimensional Hamiltonian time-periodic linear systems depending on three parameters, λ1, λ2and ε such that for ε=0 the system becomes autonomous. Using normal form techniques we study stability and bifurcations for ε>0 small enough. We pay special attention to the d'Alembert case. The results are applied to the study of the linear stability of homographic solutions of the planar three-body problem, for some homogeneous potential of degree −α, 0<α<2, including the Newtonian case.