Equipartition of eigenfunctions for boundary value problems

Patrick Gérard; Éric Leichtnam

Journées équations aux dérivées partielles (1992)

  • page 1-7
  • ISSN: 0752-0360

How to cite

top

Gérard, Patrick, and Leichtnam, Éric. "Équirépartition de fonctions propres pour des problèmes aux limites." Journées équations aux dérivées partielles (1992): 1-7. <http://eudml.org/doc/93242>.

@article{Gérard1992,
author = {Gérard, Patrick, Leichtnam, Éric},
journal = {Journées équations aux dérivées partielles},
keywords = {ergodicity; Dirichlet-Laplacian; orthonormalized eigenfunctions},
language = {fre},
pages = {1-7},
publisher = {Ecole polytechnique},
title = {Équirépartition de fonctions propres pour des problèmes aux limites},
url = {http://eudml.org/doc/93242},
year = {1992},
}

TY - JOUR
AU - Gérard, Patrick
AU - Leichtnam, Éric
TI - Équirépartition de fonctions propres pour des problèmes aux limites
JO - Journées équations aux dérivées partielles
PY - 1992
PB - Ecole polytechnique
SP - 1
EP - 7
LA - fre
KW - ergodicity; Dirichlet-Laplacian; orthonormalized eigenfunctions
UR - http://eudml.org/doc/93242
ER -

References

top
  1. [1] L. A. Bunimovitch, On the Ergodic Properties of Nowhere Dispersive Billiards, Commun. Math. Phys. 65, 295-312 (1979). Zbl0421.58017
  2. [2] Y. Colin de Verdière, Ergodicité et Fonctions propres du laplacien, Commun. Math. Phys. 102, 497-502 (1985). Zbl0592.58050MR87d:58145
  3. [3] D. Delande, in “Chaos and Quantum Physics” (Les Houches, 1989) eds. M.J. Giannoni, A. Voros et J. Zinn-Justin, North-Holland. 
  4. [4] P. Gérard, Microlocal Defect Measures, Commun. Partial Diff. Equations 16 (11), 1761-1794 (1991). Zbl0770.35001MR92k:35027
  5. [5] P. Gérard, Mesures semi-classiques et ondes de Bloch, Séminaire E.D.P., 1990-1991, exposé numéro 16, Ecole Polytechnique. Zbl0739.35096
  6. [6] P. Gérard, et E. Leichtnam, article à paraître et, Ergodicité de Fonctions Propres pour des Problèmes aux Limites. Séminaire E.D.P., 1992, Ecole Polytechnique. 
  7. [7] B. Halpern, Strange Billiards Table, Trans. AMS 232, 297-305 (1977). Zbl0374.53001MR56 #9595
  8. [8] B. Helffer, A. Martinez et D. Robert, Ergodicité et Limite semi-classique, Commun. Math. Phys. 109, 313-326 (1987). Zbl0624.58039MR88e:81029
  9. [9] M. Kac, Can one hear the shape of a drum ?, Amer. Math. Monthly 73, 1-23 (1966). Zbl0139.05603MR34 #1121
  10. [10] A. Katok, J.M. Strelcyn, Invariant Manifolds, Entropy and Billiards..., Lecture Notes in Math. 1222, Springer (1986). Zbl0658.58001MR88k:58075
  11. [11] V. F. Lazutkin, On the asymptotics of the eigenfunctions of the Laplacian, Soviet Math Dokl. 12, 1569-1572 (1971). Zbl0232.35075
  12. [12] V. F. Lazutkin, The KAM Theory and Asymptotics of spectrum of Elliptic Operators, Springer (1991). 
  13. [13] 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. [14] Ya G. Sinai, Dynamical systems with elastic reflections..., Russ. Math. Surveys 25, 137-189 (1970). Zbl0263.58011
  15. [15] A.I. Shnirelman, Ergodic Properties of eigenfunctions, Usp. Math. Naouk 29, 181-182 (1974). Zbl0324.58020MR53 #6648
  16. [16] A.I. Shnirelman, On the asymptotic proerties of eigenfunctions in the regions of chaotic motions, appendice à [12]. 
  17. [17] L. Tartar, H-measures, a new approach..., Proc. Roy. Soc. Ed., 115 A (1990), 193-230. Zbl0774.35008MR91h:35042
  18. [18] M. Taylor, Pseudo-differential Operators, Princeton (1981). MR82i:35172
  19. [19] S. Zelditch, Uniform distribution of eigenfunctions on hyperbolic surfaces, Duke Math. J. 55, 919-941 (1987). Zbl0643.58029MR89d:58129

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.