Ergodicité de fonctions propres pour des problèmes aux limites

Patrick Gérard; Eric Leichtnam

Séminaire Équations aux dérivées partielles (Polytechnique) (1991-1992)

  • page 1-12

How to cite

top

Gérard, Patrick, and Leichtnam, Eric. "Ergodicité de fonctions propres pour des problèmes aux limites." Séminaire Équations aux dérivées partielles (Polytechnique) (1991-1992): 1-12. <http://eudml.org/doc/112031>.

@article{Gérard1991-1992,
author = {Gérard, Patrick, Leichtnam, Eric},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {ergodic theory; eigenfunctions; billiard problem},
language = {fre},
pages = {1-12},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Ergodicité de fonctions propres pour des problèmes aux limites},
url = {http://eudml.org/doc/112031},
year = {1991-1992},
}

TY - JOUR
AU - Gérard, Patrick
AU - Leichtnam, Eric
TI - Ergodicité de fonctions propres pour des problèmes aux limites
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1991-1992
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 12
LA - fre
KW - ergodic theory; eigenfunctions; billiard problem
UR - http://eudml.org/doc/112031
ER -

References

top
  1. [B] L.A. Bunimovitch, On the Ergodic properties of Nowhere Dispersive Billiards, Commun. Math. Phys.65, 295-312 (1979). Zbl0421.58017MR530154
  2. [C] Y. Colin de Verdière, Ergodicité et fonctions propres du laplacien, Commun. Math. Phys.102, 497-502 (1985). Zbl0592.58050MR818831
  3. [D] D. Delande, in "Chaos and Quantum Physics" (Les Houches, 1989) eds. M.J. Giannoni, A. Voros et J. Zinn-Justin, North-Holland (1991). Zbl0982.81023
  4. [G1] P. Gérard, Microlocal Defect Measures, Commun. Partial Diff. Equations16 (11), 1761-1794 (1991). Zbl0770.35001MR1135919
  5. [G2] P. Gérard, Mesures semi-classiques et ondes de Bloch, Séminaire Equations aux Dérivées Partielles, 1990- 1991, exposé n° XVI, Ecole Polytechnique. Zbl0739.35096MR1131589
  6. [Ha] B. Halpern, Strange billiards table, Trans. AMS232, 297-305 (1977). Zbl0374.53001MR451308
  7. [HMR] B. Helffer, A., Martinez et D. Robert, Ergodicité et limite semi-classique, Commun Math. Phys.109, 313-326 (1987). Zbl0624.58039MR880418
  8. [H] J.W. Helton, An operator algebra approach to partial differential equations..., Indiana Univ. Math J.26, 997-1018 (1977). Zbl0373.35060MR494325
  9. [Kac] M. Kac, Can one hear the shape of a drum, Amer. Math. Monthly73, 1-23 (1966). Zbl0139.05603MR201237
  10. [KS] A. Katok, J.-M. Strelcyn, Invariant Manifolds, Entropy and Billiards...., Lecture Notes in Math.1222, Springer (1986). Zbl0658.58001
  11. [L1] V.F. Lazutkin, On the asymptotics of the eigenfunctions of the Laplacian, Soviet Math Dokl.12, 1569-1572 (1971). Zbl0232.35075
  12. [L2] V.F. Lazutkin, The KAM theory and Asymptotics of Spectrum of elliptic operators, Springer (1991). 
  13. [LV] P. Leboeuf et A. Voros, Multiplicative formulation of Quantum Mechanics: a new setting for Semi-classical Analysis, actes du Colloque Franco-Japonais: "Analyse algébrique des perturbations singulières", CIRM, Luminy, 21-26 oct.1991. Zbl0832.35120
  14. [Si] Ya G. Sinai, Dynamical systems with elastic reflections..., Russ. Math. Surveys25, 137-189 (1970). Zbl0263.58011
  15. [S1] A.I. Shnirelman, Ergodic Properties of Eigenfunctions, Usp. Mat. Naouk29, 181-182 (1974). MR402834
  16. [S2] A.I. Shnirelman, On the asymptotic properties of eigenfunctions in the regions of chaotic motions, appendice à [L2]. 
  17. [T] L. Tartar, H-measures, a new approach..., Proc. Roy. Soc. Ed., 115A (1990), 193-230. Zbl0774.35008MR1069518
  18. [Tay] M. Taylor, Pseudodifferential Operators, Princeton (1981). Zbl0453.47026MR618463
  19. [Z] S. Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J.55, 919-941 (1987). Zbl0643.58029MR916129

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.