Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit   In this paper, we prove Morse index theorem of Lagrangian system with any
self-adjoint boundary conditions. Based on it, we give some nontrivial
estimation on the difference of Morse indices. As an application, we get a new
criterion for the stability problem of brake periodic orbit.

31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
1
The categories of this paper are: cs