Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Hessian limit directions along non-oscillating gradient trajectories   Given a non-oscillating gradient trajectory G of a real analytic function f,
we show that the limit v of the secants at the limit point O of G along the
trajectory G is an eigen-vector of the limit of the direction of the Hessian
matrix Hess (f) at O along G. The same holds true at infinity if the function
is globally subanalytic. We also deduce some interesting estimates along the
trajectory.

13
The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th