Entropy of Semiclassical Measures for Nonpositively Curved Surfaces |
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| Authors: | Gabriel Rivière |
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| Institution: | 1. Centre de Mathématiques Laurent Schwartz (UMR 7640), école Polytechnique, 91128, Palaiseau Cedex, France
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| Abstract: | We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive
sectional curvature. To do this, we look at sequences of distributions associated to them and we study the entropic properties
of their accumulation points, the so-called semiclassical measures. Precisely, we show that the Kolmogorov–Sinai entropy of
a semiclassical measure μ for the geodesic flow g
t
is bounded from below by half of the Ruelle upper bound, i.e.
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hKS(m,g) 3 \frac12 òS*M c+(r) d m(r),h_{KS}(\mu,g)\geq \frac{1}{2} \int\limits_{S^*M} \chi^+(\rho) {\rm d} \mu(\rho), |
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| Keywords: | |
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