Integrability of C¹ invariant splittings

الأصل · EN

We derive some new conditions for integrability of dynamically defined C¹ invariant splittings in arbitrary dimension and co-dimension. In particular we prove that every 2-dimensional C¹ 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.