Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measure rigidity beyond uniform hyperbolicity: Invariant Measures for
  Cartan actions on Tori   We prove that every smooth action of Z^k, k>1, on the (k+1)-dimensional torus
homotopic to an action by hyperbolic linear maps preserves an absolutely
continuous measure. This is a first known result concerning abelian groups of
diffeomorphisms where existence of an invariant geometric structure is obtained
from homotopy data.

31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org