Dominated Splittings for Flows with singularities

Abstract

We obtain sufficient conditions for an invariant splitting over a compact invariant subset of a $C^1$ flow $X_t$ to be dominated. In particular, we reduce the requirements to obtain sectional hyperbolicity and hyperbolicity.

arXiv comment15 pages, 4 figures; streamlined presentation; statement and proof of main theorem corrected; included new application to obtain hyperbolicity for three-dimensional flows; some corrections suggested by the referee