Entropy of eigenfunctions of the Laplacian in dimension 2
Journées équations aux dérivées partielles (2010), Exposé no. 15, 17 p.
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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 for the geodesic flow is bounded from below by half of the Ruelle upper bound. (This text has been written for the proceedings of the Journées EDP (Port d’Albret-June, 7-11 2010))
@incollection{JEDP_2010____A15_0,
author = {Rivi\`ere, Gabriel},
title = {Entropy of eigenfunctions of the {Laplacian} in dimension 2},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:15},
pages = {1--17},
year = {2010},
publisher = {Groupement de recherche 2434 du CNRS},
doi = {10.5802/jedp.72},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/jedp.72/}
}
TY - JOUR AU - Rivière, Gabriel TI - Entropy of eigenfunctions of the Laplacian in dimension 2 JO - Journées équations aux dérivées partielles N1 - talk:15 PY - 2010 SP - 1 EP - 17 PB - Groupement de recherche 2434 du CNRS UR - http://geodesic.mathdoc.fr/articles/10.5802/jedp.72/ DO - 10.5802/jedp.72 LA - en ID - JEDP_2010____A15_0 ER -
%0 Journal Article %A Rivière, Gabriel %T Entropy of eigenfunctions of the Laplacian in dimension 2 %J Journées équations aux dérivées partielles %Z talk:15 %D 2010 %P 1-17 %I Groupement de recherche 2434 du CNRS %U http://geodesic.mathdoc.fr/articles/10.5802/jedp.72/ %R 10.5802/jedp.72 %G en %F JEDP_2010____A15_0
Rivière, Gabriel. Entropy of eigenfunctions of the Laplacian in dimension 2. Journées équations aux dérivées partielles (2010), Exposé no. 15, 17 p.. doi: 10.5802/jedp.72
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