Luciana Salgado

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

Singular hyperbolicity and sectional Lyapunov exponents of various orders

DX

ON INVARIANT DECOMPOSITIONS, DOMINATED SPLITTINGS AND SECTIONAL-HYPERBOLICITY

of the vector field

Adapted metrics for singular hyperbolic flows

X

Infinitesimal Lyapunov functions and singular-hyperbolicity for three-dimensional flows

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.

Infinitesimal Lyapunov functions and singular-hyperbolicity

We obtain sufficient conditions for an invariant splitting over a compact invariant subset of a C1 flow Xt to be dominated. In particular, we reduce the requirements to obtain sectional hyperbolicity and hyperbolicity.