Entropy of semiclassical measures for nonpositively curved surfaces

Details Entropy of semiclassical measures for nonpositively curved surfaces Entropy of semiclassical measures for nonpositively curved surfaces

2009-11-10

arxiv.org/abs/0911.1840v1

Annales Henri Poincar\'e 11 (2010) 1085-1116

Mathematics

Dynamical Systems

20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version

Scientific paper

10.1007/s00023-010-0055-2

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.

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