Integrability of C^1 invariant splittings
  We derive some new conditions for integrability of dynamically defined C^1 invariant splittings in arbitrary dimension and co-dimension. In particular we prove that every 2-dimensional C^1 invariant decomposition on a 3-dimensional manifold satisfying a volume domination condition is uniquely integrable. In the special case of volume preserving diffeomorphisms we show that standard dynamical domination is already sufficient to guarantee unique integrability. 
Stefano Luzzatto, Sina Tureli, Khadim War
math.DS