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On the Minimality of Keplerian Arcs with Fixed Negative Energy
Qualitative Theory of Dynamical Systems ( IF 1.4 ) Pub Date : 2020-02-07 , DOI: 10.1007/s12346-020-00362-9
Vivina Barutello , Alberto Boscaggin , Walter Dambrosio

We revisit a classical result by Jacobi (J Reine Angew Math 17:68–82, 1837) on the local minimality, as critical points of the corresponding energy functional, of fixed-energy solutions of the Kepler equation joining two distinct points with the same distance from the origin. Our proof relies on the Morse index theorem, together with a characterization of the conjugate points as points of geodesic bifurcation.

中文翻译:

具有固定负能量的开普勒弧的极小性

我们重新审视了Jacobi的经典结果(J Reine Angew Math 17:68–82,1837),它作为两个相应点的开普勒方程固定能量解的局部极小值,作为相应能量泛函的临界点,距原点的距离。我们的证明依赖于摩尔斯指数定理,以及共轭点作为测地线分叉点的特征。
更新日期:2020-02-07
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