Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the stability of Ma\~n\'e critical hypersurfaces   We construct examples of Tonelli Hamiltonians on $\T^n$ (for any $n\geq 2$)
such that the hypersurfaces corresponding to the Ma\~n\'e critical value are
stable (i.e. geodesible). We also provide a criterion for instability in terms
of closed orbits in free homotopy classes and we show that any stable energy
level of a Tonelli Hamiltonian must contain a closed orbit.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con