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dc.contributor.author |
Montgomery, R. |
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dc.date.accessioned |
2019-02-09T21:00:43Z |
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dc.date.available |
2019-02-09T21:00:43Z |
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dc.date.issued |
2014 |
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dc.identifier.citation |
Who's Afraid of the Hill Boundary?/ R. Montgomery // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 8 назв. — англ. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 37J50; 58E10; 70H99; 37J45; 53B50 |
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dc.identifier.other |
DOI:10.3842/SIGMA.2014.101 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/146540 |
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dc.description.abstract |
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. |
uk_UA |
dc.description.sponsorship |
I thank Mark Levi and Mikhail Zhitomirskii for helpful e-mail conversations. I acknowledge
NSF grant DMS-1305844 for support. |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
Who's Afraid of the Hill Boundary? |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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