Who's Afraid of the Hill Boundary?
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Who's Afraid of the Hill Boundary?
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| Creator |
Montgomery, R.
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| Description |
The Jacobi-Maupertuis metric allows one to reformulate Newton's equations as geodesic equations for a Riemannian metric which degenerates at the Hill boundary. We prove that a JM geodesic which comes sufficiently close to a regular point of the boundary contains pairs of conjugate points close to the boundary. We prove the conjugate locus of any point near enough to the boundary is a hypersurface tangent to the boundary. Our method of proof is to reduce analysis of geodesics near the boundary to that of solutions to Newton's equations in the simplest model case: a constant force. This model case is equivalent to the beginning physics problem of throwing balls upward from a fixed point at fixed speeds and describing the resulting arcs, see Fig. 2.
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| Date |
2019-02-09T21:00:43Z
2019-02-09T21:00:43Z 2014 |
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| Type |
Article
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| Identifier |
Who's Afraid of the Hill Boundary?/ R. Montgomery // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 8 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 37J50; 58E10; 70H99; 37J45; 53B50 DOI:10.3842/SIGMA.2014.101 http://dspace.nbuv.gov.ua/handle/123456789/146540 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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