Abstract We outline the flexibility program in smooth dynamics, focusing on of Lyapunov exponents for volume-preserving diffeomorphisms. prove results Anosov diffeomorphisms admitting dominated splittings into one-dimensional bundles.

The paper relates set-valued Lyapunov functions to pointwise asymptotic stability in systems described by a difference inclusion. Pointwise asymptotic stability of a set is a property which requires that each point of the set be Lyapunov stable and that every solution to the inclusion, from a neighborhood of the set, be convergent and have the limit in the set. Weak set-valued Lyapunov function...