Infinitesimal Lyapunov functions for singular flows
  We present an extension of the notion of infinitesimal Lyapunov function to singular flows, and from this technique we deduce a characterization of partial/sectional hyperbolic sets. In absence of singularities, we can also characterize uniform hyperbolicity.   These conditions can be expressed using the space derivative DX of the vector field X together with a field of infinitesimal Lyapunov functions only, and are reduced to checking that a certain symmetric operator is positive definite at the tangent space of every point of the trapping region. 
Vitor Araujo and Luciana Salgado
math.DS math.CA