Infinitesimal Lyapunov functions for singular flows

摘要

We present an extension of the notion of infinitesimal Lyapunov function tosingular flows, and from this technique we deduce a characterization ofpartial/sectional hyperbolic sets. In absence of singularities, we can alsocharacterize uniform hyperbolicity. These conditions can be expressed using the space derivative DX of the vectorfield X together with a field of infinitesimal Lyapunov functions only, and arereduced to checking that a certain symmetric operator is positive definite atthe tangent space of every point of the trapping region.