English

Entropy of semiclassical measures in dimension 2

Mathematical Physics 2019-12-19 v3 Dynamical Systems math.MP

Abstract

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of Anosov type. 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

Cite

@article{arxiv.0809.0230,
  title  = {Entropy of semiclassical measures in dimension 2},
  author = {Gabriel Riviere},
  journal= {arXiv preprint arXiv:0809.0230},
  year   = {2019}
}

Comments

42 pages, 3 figures. Compared to the second version, I have removed the proof in the case of surfaces of nonpositive curvature and I have written it in a different article (arXiv:0911.1840)

R2 v1 2026-06-21T11:15:40.047Z