Entropy of eigenfunctions of the Laplacian in dimension 2

Gabriel Rivière[1]

  • [1] Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau Cedex, France

Journées Équations aux dérivées partielles (2010)

  • Volume: 155, Issue: 2, page 1-17
  • ISSN: 0752-0360

Abstract

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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 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))

How to cite

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Rivière, Gabriel. "Entropy of eigenfunctions of the Laplacian in dimension 2." Journées Équations aux dérivées partielles 155.2 (2010): 1-17. <http://eudml.org/doc/116381>.

@article{Rivière2010,
abstract = {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 $\mu $ 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 $37^\{\text\{èmes\}\}$ Journées EDP (Port d’Albret-June, 7-11 2010))},
affiliation = {Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau Cedex, France},
author = {Rivière, Gabriel},
journal = {Journées Équations aux dérivées partielles},
keywords = {Laplacian; compact Riemannian surface; Kolmogorov-Sinai entropy; geodesic flow; semiclassical measure},
language = {eng},
month = {6},
number = {2},
pages = {1-17},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Entropy of eigenfunctions of the Laplacian in dimension 2},
url = {http://eudml.org/doc/116381},
volume = {155},
year = {2010},
}

TY - JOUR
AU - Rivière, Gabriel
TI - Entropy of eigenfunctions of the Laplacian in dimension 2
JO - Journées Équations aux dérivées partielles
DA - 2010/6//
PB - Groupement de recherche 2434 du CNRS
VL - 155
IS - 2
SP - 1
EP - 17
AB - 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 $\mu $ 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 $37^{\text{èmes}}$ Journées EDP (Port d’Albret-June, 7-11 2010))
LA - eng
KW - Laplacian; compact Riemannian surface; Kolmogorov-Sinai entropy; geodesic flow; semiclassical measure
UR - http://eudml.org/doc/116381
ER -

References

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