Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.
- [1] Centre de Mathématiques, Ecole Polytechnique, F - 91128 - Palaiseau cedex
Séminaire Équations aux dérivées partielles (2000-2001)
- Volume: 2000-2001, page 1-8
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topSjöstrand, Johannes. "Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.." Séminaire Équations aux dérivées partielles 2000-2001 (2000-2001): 1-8. <http://eudml.org/doc/11012>.
@article{Sjöstrand2000-2001,
affiliation = {Centre de Mathématiques, Ecole Polytechnique, F - 91128 - Palaiseau cedex},
author = {Sjöstrand, Johannes},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Bohr-Sommerfeld quantization condition; smooth symbol; KAM theorem},
language = {eng},
pages = {1-8},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.},
url = {http://eudml.org/doc/11012},
volume = {2000-2001},
year = {2000-2001},
}
TY - JOUR
AU - Sjöstrand, Johannes
TI - Bohr–Sommerfeld quantization condition for non-selfadjoint operators in dimension 2.
JO - Séminaire Équations aux dérivées partielles
PY - 2000-2001
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2000-2001
SP - 1
EP - 8
LA - eng
KW - Bohr-Sommerfeld quantization condition; smooth symbol; KAM theorem
UR - http://eudml.org/doc/11012
ER -
References
top- A. Bazzani, G. Turchetti, Singularities of normal forms and topology of orbits in area-preserving maps, J. Phys. A, 25(8)(1992), 427–432. Zbl0761.58009MR1162865
- L. Bers, F. John, M. Schechter, Partial differential equations, Reprint of the 1964 original. Lectures in Applied Mathematics, AMS, Providence, R.I., 1979. Zbl0514.35001MR163043
- E. Chirka, seminar talk in Gothenburg, April 2000.
- Y. Colin de Verdière, Quasi-modes sur les variétés Riemanniennes, Inv. Math., 43(1)(1977), 15–52. Zbl0449.53040MR501196
- 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. Zbl0916.34071MR1635811
- C. Gérard, J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type, Comm. Math. Phys., 108(1987), 391–421. Zbl0637.35027MR874901
- A. Grigis, J. Sjöstrand, Microlocal analysis for differential operators, London Math. Soc. Lecture Notes Series 196, Cambridge Univ. Press, 1994. Zbl0804.35001MR1269107
- B. Helffer, D. Robert, Puits de potentiel généralisés et asymptotique semiclassique, Ann. Henri Poincaré, Phys. Th., 41(3)(1984), 291–331. Zbl0565.35082MR776281
- B. Helffer, J. Sjöstrand, Résonances en limite semiclassique, Bull. de la SMF 114(3), Mémoire 24/25(1986). Zbl0631.35075
- N. Kaidi, Ph. Kerdelhué, Forme normale de Birkhoff et résonances, Asympt. Anal., 23(2000), 1–21. Zbl0955.35009MR1764337
- A. Lahmar-Benbernou, A. Martinez, On Helffer–Sjöstrand’s theory of resonances, Preprint March 2001.
- L. Landau, B. Lifschitz, Mécanique quantique, théorie non relativiste, Editions Mir, Moscou 1966. Zbl0144.47605
- 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. Zbl0814.58001MR1239173
- A. Melin, J, Sjöstrand, Determinants of pseudodifferential operators and complex deformations of phase space, Preprint, Jan. 2001. Zbl1082.35176MR1957486
- 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. Zbl0970.37050MR1770799
- 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. Zbl1002.37028MR1770800
- J. Sjöstrand, Semi-excited states in nondegenerate potential wells, Asymptotic Analysis, 6(1992), 29–43. Zbl0782.35050MR1188076
- J. Sjöstrand, Singularités analytiques microlocales, Astérisque, 95(1982). Zbl0524.35007MR699623
- 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. Zbl0889.46027MR1445350
- J. Sjöstrand, Semiclassical resonances generated by a non-degenerate critical point, Springer LNM 1256, 402–429. Zbl0627.35074MR897789
- S. Vu-Ngoc, Invariants symplectiques et semi-classiques des systèmes intégrables avec singularité, Séminaire e.d.p., Ecole Polytechnique, 23 janvier, 2000–2001. Zbl1072.37047MR1860684
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