On the minimality of Keplerian arcs with fixed negative energy
| Autor: | Vivina Barutello, Alberto Boscaggin, Walter Dambrosio |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Geodesic Applied Mathematics Conjugate points Kepler's equation Characterization (mathematics) 01 natural sciences 010101 applied mathematics symbols.namesake Mathematics - Classical Analysis and ODEs 0103 physical sciences symbols Classical Analysis and ODEs (math.CA) FOS: Mathematics Discrete Mathematics and Combinatorics Negative energy 0101 mathematics 010301 acoustics Atiyah–Singer index theorem Bifurcation Mathematics Energy functional |
| DOI: | 10.48550/arxiv.1910.06681 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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