Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Who's Afraid of the Hill Boundary?   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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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat