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  • Séminaire Laurent Schwartz — EDP et applications
  • Year 2011-2012
  • Talk no. 16
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Semi-classical measures for generalized plane waves
Colin Guillarmou1
1 DMA, U.M.R. 8553 CNRS École Normale Supérieure 45 rue d’Ulm 75230 Paris cedex 05 France
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Talk no. 16, 9 p.
  • Abstract

Following joint work with Dyatlov [DyGu], we describe the semi-classical measures associated with generalized plane waves for metric perturbation of ℝ d , under the condition that the geodesic flow has trapped set K of Liouville measure 0.

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DOI: 10.5802/slsedp.12
Author's affiliations:
Colin Guillarmou 1

1 DMA, U.M.R. 8553 CNRS École Normale Supérieure 45 rue d’Ulm 75230 Paris cedex 05 France
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@article{SLSEDP_2011-2012____A16_0,
     author = {Colin Guillarmou},
     title = {Semi-classical measures for generalized plane waves},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:16},
     pages = {1--9},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2011-2012},
     doi = {10.5802/slsedp.12},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.12/}
}
TY  - JOUR
AU  - Colin Guillarmou
TI  - Semi-classical measures for generalized plane waves
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:16
PY  - 2011-2012
SP  - 1
EP  - 9
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.12/
DO  - 10.5802/slsedp.12
LA  - en
ID  - SLSEDP_2011-2012____A16_0
ER  - 
%0 Journal Article
%A Colin Guillarmou
%T Semi-classical measures for generalized plane waves
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:16
%D 2011-2012
%P 1-9
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.12/
%R 10.5802/slsedp.12
%G en
%F SLSEDP_2011-2012____A16_0
Colin Guillarmou. Semi-classical measures for generalized plane waves. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Talk no. 16, 9 p. doi : 10.5802/slsedp.12. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.12/
  • References
  • Cited by

[Bu] N. Burq, Décroissance de l’énergie locale de l’équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel. Acta Math. 180 (1998), no. 1, 1–29. | MR | Zbl

[CdV] Y. Colin de Verdière, Ergodicité et fonctions propres du Laplacien, Comm. Math. Phys. 102(1985), no. 3, 497–502. | MR | Zbl

[DyGu] S. Dyatlov, C. Guillarmou, Microlocal limits of plane waves and Eisenstein functions, arXiv:1204.1305.

[HeMaRo] B. Helffer, A. Martinez, and D. Robert, Ergodicité en limite semi-classique, Comm. Math. Phys. 109(1987), no. 2, 313–326. | MR | Zbl

[Ma] A. Martinez, An Introduction to Semiclassical and Microlocal Analysis, Springer-Verlag New–York, UTX Series, 2002. | MR | Zbl

[Me] R.B. Melrose, Geometric scattering theory, Lectures at Stanford, Cambridge University Press. | MR | Zbl

[Sh] A.I. Shnirelman, Ergodic properties of eigenfunctions, Usp. Mat. Nauk. 29(1974), 181–182. | MR | Zbl

[Ze87] S. Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55(1987), no. 4, 919–941. | MR | Zbl

[Zw] M. Zworski, Semiclassical analysis, to appear in Graduate Studies in Mathematics, AMS, 2012, http://math.berkeley.edu/~zworski/semiclassical.pdf. | MR | Zbl

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