Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic and contact properties of the Ma\~n\'e critical value of the
  universal cover   We discuss several symplectic aspects related to the Ma\~n\'e critical value
c_u of the universal cover of a Tonelli Hamiltonian. In particular we show that
the critical energy level is never of virtual contact type for manifolds of
dimension greater than or equal to three. We also show the symplectic
invariance of the finiteness of the Peierls barrier and the Aubry set of the
universal cover. We also provide an example where c_u coincides with the
infimum of Mather's \alpha -function but the Aubry set of the universal cover
is empty and the Peierls barrier is finite. A second example exhibits all the
ergodic invariant minimizing measures with zero homotopy, showing that, quite
surprisingly, the union of their supports is not a graph, in contrast with
Mather's celebrated graph theorem.

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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex