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Geodesic flows modelled by expansive flows. (English) Zbl 1421.53084

Summary: Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow with a local product structure such that the semi-conjugation preserves time parametrization. It is concluded that the geodesic flow has a unique measure of maximal entropy.

MSC:

53D25 Geodesic flows in symplectic geometry and contact geometry
53C22 Geodesics in global differential geometry
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
28D20 Entropy and other invariants
28D99 Measure-theoretic ergodic theory
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