On the Minimality of Keplerian Arcs with Fixed Negative Energy

• Barutello Vivina ^[1] ; Boscaggin Alberto ^[1] ; Dambrosio, Walter ^[1]
  1. [1] Università di Torino
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
• DOI: 10.1007/s12346-020-00362-9
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• Resumen

  • 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.

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