Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Summary on Symmetries and Conserved Quantities of Autonomous
  Hamiltonian Systems,   A complete geometric classification of symmetries of autonomous Hamiltonian
mechanical systems is established; explaining how to obtain their associated
conserved quantities in all cases. In particular, first we review well-known
results and properties about the symmetries of the Hamiltonian and of the
symplectic form and then some new kinds of non-symplectic symmetries and their
conserved quantities are introduced and studied.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess