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