Lyapunov-like functions and geodesic flows (Q1100793)

The author is interested mainly in obtaining good criteria for a given system to be Anosov, and proves first a proposition which gives a criterion for vector bundle homeomorphisms to be quasi-hyperbolic. By applying this result to geodesic flows, the author gives a sufficient condition for geodesic flows to be Anosov. This criterion may be applied to Riemann manifolds with small patches of small positive curvatures. The author also applies this method to obtain a generalization of Chicone's criterion for geodesic flows to be Anosov.