English

On the minimality of Keplerian arcs with fixed negative energy

Classical Analysis and ODEs 2019-10-16 v1

Abstract

We revisit a classical result by Jacobi 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.

Keywords

Cite

@article{arxiv.1910.06681,
  title  = {On the minimality of Keplerian arcs with fixed negative energy},
  author = {Vivina Barutello and Alberto Boscaggin and Walter Dambrosio},
  journal= {arXiv preprint arXiv:1910.06681},
  year   = {2019}
}