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Entropy of semiclassical measures in dimension 2. (English) Zbl 1230.37048

On a compact Riemannian surface with a geodesic flow of Anosov type the high energy asymptotic properties of the Laplacian are considered. It is shown that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound.

MSC:

37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
58J51 Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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References:

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