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Invariant two-forms for geodesic flows. (English) Zbl 0821.58033

Let \(M\) be an \(n\)-dimensional compact Riemannian manifold of negative sectional curvature with Anosov splitting of class \(C^ 1\). We investigate the space of continuous two-forms on the unit tangent bundle \(T^ 1 M\) of \(M\) which are invariant under the action of the geodesic flow. As an application we show that the metric and the topological entropy of the geodesic flow on \(T^ 1 M\) coincide if the Anosov splitting is of class \(C^ 2\).

MSC:

37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
53C22 Geodesics in global differential geometry
54C70 Entropy in general topology
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References:

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