Semi-classical measures for generalized plane waves

Colin Guillarmou[1]

  • [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)

  • Volume: 2011-2012, page 1-9
  • ISSN: 2266-0607

Abstract

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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 .

How to cite

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Guillarmou, Colin. "Semi-classical measures for generalized plane waves." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-9. <http://eudml.org/doc/251163>.

@article{Guillarmou2011-2012,
abstract = {Following joint work with Dyatlov [DyGu], we describe the semi-classical measures associated with generalized plane waves for metric perturbation of $\mathbb\{R\}^d$, under the condition that the geodesic flow has trapped set $K$ of Liouville measure $0$.},
affiliation = {DMA, U.M.R. 8553 CNRS École Normale Supérieure 45 rue d’Ulm 75230 Paris cedex 05 France},
author = {Guillarmou, Colin},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {eng},
pages = {1-9},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Semi-classical measures for generalized plane waves},
url = {http://eudml.org/doc/251163},
volume = {2011-2012},
year = {2011-2012},
}

TY - JOUR
AU - Guillarmou, Colin
TI - Semi-classical measures for generalized plane waves
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2011-2012
SP - 1
EP - 9
AB - Following joint work with Dyatlov [DyGu], we describe the semi-classical measures associated with generalized plane waves for metric perturbation of $\mathbb{R}^d$, under the condition that the geodesic flow has trapped set $K$ of Liouville measure $0$.
LA - eng
UR - http://eudml.org/doc/251163
ER -

References

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  4. B. Helffer, A. Martinez, and D. Robert, Ergodicité en limite semi-classique, Comm. Math. Phys. 109(1987), no. 2, 313–326. Zbl0624.58039MR880418
  5. A. Martinez, An Introduction to Semiclassical and Microlocal Analysis, Springer-Verlag New–York, UTX Series, 2002. Zbl0994.35003MR1872698
  6. R.B. Melrose, Geometric scattering theory, Lectures at Stanford, Cambridge University Press. Zbl0849.58071MR1350074
  7. A.I. Shnirelman, Ergodic properties of eigenfunctions, Usp. Mat. Nauk. 29(1974), 181–182. Zbl0324.58020MR402834
  8. S. Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55(1987), no. 4, 919–941. Zbl0643.58029MR916129
  9. M. Zworski, Semiclassical analysis, to appear in Graduate Studies in Mathematics, AMS, 2012, http://math.berkeley.edu/~zworski/semiclassical.pdf. Zbl1252.58001MR2952218

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