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- W3100923510 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. $$h_{KS}(mu,g)geq frac{1}{2} intlimits_{S^*M} chi^+(rho) {rm d} mu(rho),$$ where χ +(ρ) is the upper Lyapunov exponent at point ρ. The main strategy is the same as in Rivière (Duke Math J, arXiv:0809.0230, 2008) except that we have to deal with weakly chaotic behavior." @default.
- W3100923510 created "2020-11-23" @default.
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- W3100923510 date "2010-09-29" @default.
- W3100923510 modified "2023-10-08" @default.
- W3100923510 title "Entropy of Semiclassical Measures for Nonpositively Curved Surfaces" @default.
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- W3100923510 doi "https://doi.org/10.1007/s00023-010-0055-2" @default.
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