Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.
Sjöstrand, Johannes1
1 Centre de Mathématiques, Ecole Polytechnique, F - 91128 - Palaiseau cedex
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2000-2001), Exposé no. 16, 8 p.
Sjöstrand, Johannes 1

1 Centre de Mathématiques, Ecole Polytechnique, F - 91128 - Palaiseau cedex 
@article{SEDP_2000-2001____A16_0,
     author = {Sj\"ostrand, Johannes},
     title = {Bohr{\textendash}Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:16},
     pages = {1--8},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2000-2001},
     zbl = {1066.53141},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2000-2001____A16_0/}
}
TY  - JOUR
AU  - Sjöstrand, Johannes
TI  - Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:16
PY  - 2000-2001
SP  - 1
EP  - 8
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/item/SEDP_2000-2001____A16_0/
LA  - en
ID  - SEDP_2000-2001____A16_0
ER  - 
%0 Journal Article
%A Sjöstrand, Johannes
%T Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:16
%D 2000-2001
%P 1-8
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://www.numdam.org/item/SEDP_2000-2001____A16_0/
%G en
%F SEDP_2000-2001____A16_0
Sjöstrand, Johannes. Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2000-2001), Exposé no. 16, 8 p. http://www.numdam.org/item/SEDP_2000-2001____A16_0/

[BaTu] A. Bazzani, G. Turchetti, Singularities of normal forms and topology of orbits in area-preserving maps, J. Phys. A, 25(8)(1992), 427–432. | MR | Zbl

[BeJoSc] L. Bers, F. John, M. Schechter, Partial differential equations, Reprint of the 1964 original. Lectures in Applied Mathematics, AMS, Providence, R.I., 1979. | MR | Zbl

[Ch] E. Chirka, seminar talk in Gothenburg, April 2000.

[Co] Y. Colin de Verdière, Quasi-modes sur les variétés Riemanniennes, Inv. Math., 43(1)(1977), 15–52. | MR | Zbl

[FuRa] S. Fujiie, T. Ramond, Matrice de scattering et résonances associées à une orbite hétérocline, Ann. Inst. H. Poincaré, Phys. Théor., 69(1)(1998), 31–82. | Numdam | MR | Zbl

[GeSj] C. Gérard, J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type, Comm. Math. Phys., 108(1987), 391–421. | MR | Zbl

[GrSj] A. Grigis, J. Sjöstrand, Microlocal analysis for differential operators, London Math. Soc. Lecture Notes Series 196, Cambridge Univ. Press, 1994. | MR | Zbl

[HeRo] B. Helffer, D. Robert, Puits de potentiel généralisés et asymptotique semiclassique, Ann. Henri Poincaré, Phys. Th., 41(3)(1984), 291–331. | Numdam | MR | Zbl

[HeSj] B. Helffer, J. Sjöstrand, Résonances en limite semiclassique, Bull. de la SMF 114(3), Mémoire 24/25(1986). | Numdam | Zbl

[KaKe] N. Kaidi, Ph. Kerdelhué, Forme normale de Birkhoff et résonances, Asympt. Anal., 23(2000), 1–21. | MR | Zbl

[LahMa] A. Lahmar-Benbernou, A. Martinez, On Helffer–Sjöstrand’s theory of resonances, Preprint March 2001.

[LaLi] L. Landau, B. Lifschitz, Mécanique quantique, théorie non relativiste, Editions Mir, Moscou 1966. | Zbl

[Laz] V.F. Lazutkin, KAM theory and semiclassical approximations to eigenfunctions. With an addendum by A. I. Shnirelman. Ergebnisse der Mathematik und ihrer Grenzgebiete, 24. Springer-Verlag, Berlin, 1993. | MR | Zbl

[MeSj] A. Melin, J, Sjöstrand, Determinants of pseudodifferential operators and complex deformations of phase space, Preprint, Jan. 2001. | MR

[Po1] G. Popov, Invariant tori, effective stability, and quasimodes with exponentially small error terms. I. Birkhoff normal forms, Ann. Henri Poincaré, Phys. Th., 1(2)(2000), 223–248. | MR | Zbl

[Po2] G. Popov, Invariant tori, effective stability, and quasimodes with exponentially small error terms. II. Quantum Birkhoff normal forms, Ann. Henri Poincaré, Phys. Th., 1(2)(2000), 249–279. | MR | Zbl

[Sj] J. Sjöstrand, Semi-excited states in nondegenerate potential wells, Asymptotic Analysis, 6(1992), 29–43. | MR | Zbl

[Sj2] J. Sjöstrand, Singularités analytiques microlocales, Astérisque, 95(1982). | Numdam | MR | Zbl

[Sj3] J. Sjöstrand, Function spaces associated to global I-Lagrangian manifolds, pages 369-423 in Structure of solutions of differential equations, Katata/Kyoto, 1995, World Scientific 1996. | MR | Zbl

[Sj4] J. Sjöstrand, Semiclassical resonances generated by a non-degenerate critical point, Springer LNM 1256, 402–429. | MR | Zbl

[Vu] S. Vu-Ngoc, Invariants symplectiques et semi-classiques des systèmes intégrables avec singularité, Séminaire e.d.p., Ecole Polytechnique, 23 janvier, 2000–2001. | Numdam | MR | Zbl