Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear instability of periodic orbits of free period Lagrangian systems   In this paper we provide a sufficient condition for the linear instability of
a periodic orbit for a free period Lagrangian system on a Riemannian manifold.
  The main result establish a general criterion for the linear instability of a
maybe degenerate) periodic orbit admitting a orbit cylinder in terms to the
parity of a suitable spectral index encoding the functional and symplectic
property of the problem.

32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
3
The categories of this paper are: physics