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The search for tractable models led to the study of the free motion of a particle (the geodesic flow) on surfaces of constant negative curvature.
Let us insist that special loci, which are the fixed-point sets of the action of the modular group are simultaneously algebraic, arithmetic and totally geodesic.
Since expansive geodesic flows of compact surfaces have no conjugate points, the accessibility property holds for every two-dimensional expansive geodesic flow.
We show that the metric of non-positively curved graph manifolds is determined by its geodesic flow.
Quasiconformality in the geodesic flow of negatively curved manifolds.
It follows from this that the times at which the geodesic crosses itself are isolated.
Neither do geometric geodesics prescribe our perceptual solutions in more than a few specialized cases.
A curve that satisfies (17) will be called a magnetic geodesic.
The geodesic flows constructed here do have positive topological entropy because they contain horseshoes.
The geodesic flow for this perturbed metric will have positive topological entropy because it contains a horseshoe.
Curvature bounds for the entropy of the geodesic flow on a surface.
Among his famous successes is the geodesic flow on an ellipsoid, which he found to be integrable.
An invariant chronometric law finally becomes possible when critical times are related to distances along the appropriate geodesic paths in the appropriate representational space.
One way to prove lower bounds for the expansion rate of symmetrical graphs is based on the enumeration of geodesics.
From this we derive applications to geodesic flows on manifolds of constant negative curvature.
