Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational principle and phase space measure in non-canonical
  coordinates   Non-canonical equations of motion are derived from a variational principle
written in symplectic form. The invariant measure of phase space and the
covariant expression for the entropy are derived from non-canonical
transformations of coordinates. This shows that the geometry of non-canonical
phase space is non trivial even if dynamics has no compressibility.

24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas