From this we derive applications to geodesic flows on manifolds of constant negative curvature.
One way to prove lower bounds for the expansion rate of symmetrical graphs is based on the enumeration of geodesics.
An invariant chronometric law finally becomes possible when critical times are related to distances along the appropriate geodesic paths in the appropriate representational space.
Among his famous successes is the geodesic flow on an ellipsoid, which he found to be integrable.
Curvature bounds for the entropy of the geodesic flow on a surface.
The geodesic flow for this perturbed metric will have positive topological entropy because it contains a horseshoe.
The geodesic flows constructed here do have positive topological entropy because they contain horseshoes.
A curve that satisfies (17) will be called a magnetic geodesic.
