Entropy of eigenfunctions of the Laplacian in dimension 2
Journées équations aux dérivées partielles (2010), article no. 15, 17 p.

We study asymptotic properties of eigenfunctions of the Laplacian on compact Riemannian surfaces of Anosov type (for instance negatively curved surfaces). More precisely, we give an answer to a question of Anantharaman and Nonnenmacher [4] by proving 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. (This text has been written for the proceedings of the 37 èmes Journées EDP (Port d’Albret-June, 7-11 2010))

@article{JEDP_2010____A15_0,
     author = {Rivi\`ere, Gabriel},
     title = {Entropy of eigenfunctions of the Laplacian in dimension 2},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2010},
     doi = {10.5802/jedp.72},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2010____A15_0}
}
Rivière, Gabriel. Entropy of eigenfunctions of the Laplacian in dimension 2. Journées équations aux dérivées partielles (2010), article  no. 15, 17 p. doi : 10.5802/jedp.72. http://www.numdam.org/item/JEDP_2010____A15_0/

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