Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable hierarchies and the modular class   We observe that the modular class of a Poisson-Nijhenhuis manifold has a
canonical representative and that, under a cohomological assumption, this
vector field is bi-hamiltonian. In many examples the associated hierarchy of
flows reproduces classical integrable hierarchies.

32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn