]. M. Bibliographie-[-ab-st, . A. Abramowitz-&-i, and . Stegun, Handbook of Mathematical functions with formulas, graphs and mathematical tables, pp.255-258, 1972.

]. C. Ann and . Anne, Majoration de multiplicités pour l'opérateur de Schrödinger, pp.53-60, 1989.

V. I. Arnold, Mathematical Methods of Classical Mechanics, N. 60 in GTM, 1989.

V. I. Arnold, Chapitres supplémentaires sur les EDO, 1980.

]. I. Av-pe, . Sh, . F. Averbukh-&-n, and . Perelman, Fractional revivals : universality in the long-term evolution of quantum wave packets beyond the correspondance principle dynamics, Physics Letters A, vol.139, pp.449-453, 1989.

W. Arverson, A short course on spectral theory, Graduate Texts in Mathematics, 2001.

]. W. Arv2 and . Arverson, An invitation to C*-Algebras, 1976.

M. Audin, The topology of torus action on symplectic manifolds, Progress in Math, Birkhäuser, 1991.
DOI : 10.1007/978-3-0348-7221-8

M. Audin, Les systèmes hamilitoniens et leurs intégrabilité, 2001.

]. S. Ba-we, . Bates-&-a, and . Weinstein, Lectures on the geometry of quantization, Berkeley Mathematics Lecture Notes, 1997.

]. P. Ber1 and . Berard, Variétés riemanniennes isospectrales non isométriques, Astérisque, vol.177178, pp.127-154, 1989.

]. P. Ber4, . Berard, . For-riemannian-manifolds, D. Cours-de, and G. , On ne peut pas entendre la forme d'un tambour : Introduction On ne peut pas entendre la forme d'un tambour : Exposé 1, [Ber7] P. BERARD, On ne peut pas entendre la forme d'un tambour : Exposé, 1983.

M. Berger, P. Gauduchon-&-e, and . Mazet, Le spectre d'une variété Riemannienne, Lectures Notes in Mathematics, vol.194, 1971.
DOI : 10.1007/bfb0064646

M. Berry, Some quantum-to-classical asymptotics, pp.251-303

]. G. Bes and . Besson, Sur la multiplicité de la première valeur propre des surfaces riemanniennes, Ann. Inst. Fourier, vol.30, pp.109-128, 1980.

]. J. Bil and . Bily, Propagation d'états cohérents et applications, 2001.

. R. Bkp, V. A. Bluhm, . A. Kostelecky-&-j, and . Porter, The evolution and revival structure of localized quantum wave packets, American Journal of Physics, vol.64, issue.944, 1996.

]. R. Bl-ko, . A. Bluhm-&-v, and . Kostelecky, Long term evolution and revival structure of Rydberg wave packets for hydrogen and alkali-metal atoms, Phys. Rev, vol.51, pp.4767-4786, 1995.

]. L. Bo-gu, . Boutet, &. V. De-monvel, and . Guillemin, The spectral theory of Toeplitz operators, 99 in Annals of Mathematicals, 1981.

. R. Bpu, T. Brummelhuis, . Paul-&-a, and . Uribe, Spectral estimates around a critical level, Duke Math, J, vol.78, issue.3, pp.477-530, 1995.

]. T. Car and . Carleman, Sur la théorie mathématique de l'équation de Schrödinger, Ark. Mat. Astr. Fys. 24B, vol.11, pp.1-7, 1934.

]. P. Cart and . Cartier, Introduction aux problèmes mathématiques de la mécanique quantique, 1971.

]. J. Cas and . Cassels, An introduction to diophantine approximation, Cambridge Tracts, 1957.

]. L. Ch-vun, . Charles-&-s, . Vu, and . Ngoc, Spectral asymptotics via the semiclassical birkhoff normal form, math, p.605096

]. S. Che1 and . Cheng, Eingenvalues comparison theorems and geometric applications, Math. Z, vol.143, pp.289-290, 1975.

]. S. Che2 and . Cheng, Eingenfunctions and nodal sets, Comment. Math. Helv, vol.51, pp.43-55, 1979.

Y. Colin and . Verdiere, Spectre du Laplacien et longueurs des géodésiques périodiques I, Compositio Mathematica, vol.27, pp.80-106, 1973.

Y. Colin and . Verdiere, Spectre du Laplacien et longueurs des géodésiques périodiques II, Compositio Mathematica, vol.27, pp.159-184, 1973.

]. Y. Col3, . Colin, and . Verdiere, Spectre conjoint d'opérateurs pseudodifférentiels qui commute II, Math. Z, vol.71, pp.51-73, 1980.

]. Y. Col5, ]. Y. Colin-de-verdierepa1, . Colin, &. B. De-verdiere, and . Parisse, Construction de laplaciens dont une partie finie du spectre est donnée Equilibre instable en régime semi-classique I : Concentration microlocale, Ann. Sci. Ec. Norm. Sup. Paris Comm PDE, vol.20, issue.19, pp.599-615, 1987.

]. Y. Co-pa2, . Colin, &. B. De-verdiere, and . Parisse, Equilibre instable en régime semi-classique II : Conditions de Bohr-Sommerferld, pp.347-367, 1994.

]. Y. Col6, . Colin, and . Verdiere, Le spectre du laplacien : survol partiel depuis le Berger-Gauduchon-Mazet et problèmes, Actes de la table tournante en l'honneur de Marcel Berger, Séminaires et Congrés SMF, vol.1, pp.233-252, 1996.

[. De-verdiere, M. Lombardi-&-j, and . Pollet, The microlocal Landau-Zener formula, pp.95-127, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00961343

]. Y. Co-pa3, . Colin, &. B. De-verdiere, and . Parisse, Singular Bohr-Sommerfeld rules, Commun. Math. Phys, vol.205, pp.459-500, 2000.

Y. Colin and . Verdiere, Bohr-Sommerfeld rules to all orders , Henri Poincaré Acta, pp.925-936, 2005.

]. Y. Col9, . Colin, and . Verdiere, Méthodes semi-classique et théorie spectrale, 2006.

]. Y. Col10, . Colin, and . Verdiere, Spectrum of the Laplace operator and periodic geodesics : thirty years after, Ann. Inst. Fourier, vol.57, issue.7, pp.2429-2463, 2008.

]. Y. Col11, . Colin, and . Verdiere, Semi-classical Analysis of Integrable Systems, 2008.

]. M. Co-ro, . Combescure-&-d, and . Robert, A phase study of the quantum Loschmidt Echo in the semi-classical limit, [arXiv : quant, 2005.

]. R. Co-hi, . Courant-&-d, and . Hilbert, Methods of mathematical physics, 1953.

]. S. Db-ro, &. D. De-bievre, and . Robert, Semi-classical propagation on log(¯ h) time scales, Int. Math. Res. Not, No, vol.12, pp.667-696, 2003.

]. M. Dw-le, &. P. De-wilde, and . Lecompte, Existence of star-produit and a formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds, Lett. Math.Phys, vol.7, pp.487-496, 1983.

]. M. Di-sj, . Dimassi-&-j, and . Sjöstrand, Spectral asymptotics in the semi-classical limit, Math Society Lectures Note Series 268, 1999.

]. J. Du-ho, &. L. Duistermaat, and . Hörmander, Fourier integral operators II, Acta Math, vol.128, pp.183-269, 1972.

]. L. Eli1 and . Eliasson, Hamiltonians systems withs Poisson commuting integrals, 1984.

]. L. Eli2 and . Eliasson, Normals forms for hamiltonians systems withs Poisson commuting integrals -elliptic case, Comment. Math. Helv, vol.65, pp.4-35, 1990.

]. J. Ego and . Egorov, The canonical transformation of pseudodifferential operators, pp.235-236, 1969.

]. L. Ev-zw, . Evans-&-m, and . Zworski, Lectures on semiclassical analysis

]. G. Fab and . Faber, Beweis, dass unter allen homogen Menbranen von gleicher Fläche ung gleicher Spannung die kriesförmige den tiefsten Grundton gibt, pp.169-172, 1923.

]. G. Fol and . Folland, Harmonic analysis in phase plane, 1989.

A. T. Fomenko, Integrability and Nonintegrability in Geometry and Mechanics, 1988.
DOI : 10.1007/978-94-009-3069-8

]. K. Fri and . Friedrichs, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann, vol.109, pp.465-487, 1934.

]. S. Fu-ra, . Fujiie-&-t, and . Ramond, Breit-Wigner formula at barrier tops, J. Math. Phys, vol.44, issue.5, pp.1971-1983, 2003.

]. C. Ge-gr, . Gerard-&-a, and . Grigis, Precise estimates of tunneling and eigenvalues near a potential barrier, Journal of Differential Equation, vol.72, pp.149-177, 1988.

. J. Gvzj-]-m, A. Giannoni, . Voros-&-j, and . Zinn-justin-editors, Chaos et physique théorique, Les Houches, école d'été de physique théorique 1989, session LII

]. C. Go-wi, . N. Gordon-&-e, and . Wilson, Isospectral deformations on compact manifolds, J. Diff. Geom, vol.19, pp.241-256, 1984.

C. Gordon, D. Webb-&-s, and . Wolpert, Isospectral plane domains and surfaces via Riemannian orbifolds, Inventiones Mathematicae, vol.121, issue.2, pp.1-22, 1992.
DOI : 10.1007/BF01231320

C. Gordon, D. Webb-&-s, and . Wolpert, One Cannot Hear the Shape of a Drum, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.134-138, 1992.
DOI : 10.1090/S0273-0979-1992-00289-6

]. C. Gor and . Gordon, Isospectral closed riemannian manifolds which are not localy isometric, J. Diff. Geom, vol.37, pp.639-649, 1993.

]. A. Gr-sj, . J. Grigis-&, and . Sjöstrand, Microlocal analysis and differential operators , an introduction, London Math Society Lectures Note Series 196, 1994.

]. M. Gro and . Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math, vol.82, 1985.

]. A. Gui and . Guichardet, Intégration analyse hilbertienne, Ellipses, 1989.

]. B. He-ro, . Helffer-&-d, and . Robert, Puit de potentiel généralisé et asymptotique semi-classique, Annales de l'IHP Physique Théorique, pp.291-331, 1984.

]. B. He-sj1, . Helffer-&-j, and . Sjöstrand, Multiple wells in the semi-classical limit I, Comm. in Partial Differential Equation, vol.9, issue.4, pp.337-408, 1984.

]. B. He-sj2, . Helffer-&-j, and . Sjöstrand, Semiclassical analysis of Harper's equation The weyl calculus of pseudodifferential operators, Hor1] L. HÖRMANDER, pp.360-444, 1979.

]. L. Hor2 and . Hörmander, The analysis of linear partial differential operators, pp.1983-90

]. M. Kac and . Kac, Can One Hear the Shape of a Drum?, The American Mathematical Monthly, vol.73, issue.4, pp.1-23, 1966.
DOI : 10.2307/2313748

]. T. Kat1 and . Kato, Schr??dinger operators with singular potentials, Israel Journal of Mathematics, vol.55, issue.1-2, pp.135-148, 1972.
DOI : 10.1007/BF02760233

]. T. Kat2 and . Kato, Pertubation theory for linears operators, 1980.

]. V. Ko-sh1, . A. Kondrat-'ev-&-m, and . Shubin, Discreteness of the spectrum for Schrödinger operators on manifolds of bounded, geometry Functional Analysis, Partial Differential Equations and Applications, Proceedings of the conference, 1998.

]. V. Ko-sh2, . A. Kondrat-'ev-&-m, and . Shubin, Conditions for the discreteness of the spectrum for Schrödinger operators on manifolds, Funct. Anal. and Appl, vol.33, 1999.

]. M. Kon and . Kontsevitch, Deformation quantization of Poisson manifolds, I, Preprint of the IHES [arxiv : q-alg, 1997.

]. O. Lab1 and . Lablee, Spectre du Laplacien et de l'opérateur de Schrödinger sur une variété : de la géométrie spectrale à l'analyse semi-classique, Gazette des Mathématiciens, p.116, 2008.

]. O. Lab2 and . Lablee, Sur le spectre semi-classique d'un système intégrable de dimension 1 autour d'une singularité hyperbolique, Ann. Fac. Sci. Toulouse Math., vol, vol.19, issue.1, pp.85-123, 2010.

]. F. Lau and . Laudenbach, Calcul différentiel et intégral, Editions de l'école polytechnique, 2000.

I. [. Leichtle, . Sh, . Averbukh-&-w, and . Schleich, Multilevel quantum beats: An analytical approach, Physical Review A, vol.54, issue.6, pp.5299-5312, 1996.
DOI : 10.1103/PhysRevA.54.5299

]. A. Mar and . Martinez, An introduction to Semiclassical and Microlocal Analysis, 2001.

]. C. Marz and . Marz, Spectral Asymptotics for Hill's Equation nera the potential maximum, Asymptotics Analysis, vol.5, pp.221-267, 1992.

]. D. Md-sa, &. D. Mcduff, and . Salomon, Introduction to symplectic topology, 1995.

]. J. Mil and . Milnor, Eingenvalues of the Laplace operator on certain manifolds, Proceedings of the National Academy of Sciences of the United States of America, vol.51, p.542, 1964.

]. E. Mir and . Miranda, On symplectic linearization of singular Lagragian foliation, 2003.

]. J. Mos and . Moser, The Analytic Invariants of an Area-Preserving Mapping Near a Hyperbolic Fixed Point, Comm. on pure an d applied math, pp.673-692, 1956.

]. N. Nad and . Nadirashvili, Multiple eigenvalues of the Laplace operator, Math. USSR Sbornik, vol.61, pp.225-238, 1988.

]. I. Ole1 and . Oleinik, On the essential self-adjointness of the Schrödinger operators on a complete Riemannian manifold, Math. Notes, vol.54, pp.934-939, 1993.

I. M. Oleinik, On the connection of the classical and quantum mechanical completeness of a potential at infinity on complete Riemannian manifolds, Mathematical Notes, vol.60, issue.No. 1, pp.380-386, 1994.
DOI : 10.1007/BF02112477

]. I. Ole3 and . Oleinik, On the essential self-adjointness of the Schrödinger-type operators on a complete Riemannian manifold, 1997.

T. Paul, Echelles de temps pour l'évolution quantique à petite constante de planck, Séminaire X-EDP, 2007.

]. T. Pau2 and . Paul, Reconstruction and non-reconstruction of wave packets, 2008.

]. T. Pau3 and . Paul, Reconstruction of wave packets on a hyperbolic trajectory, 2008.

]. T. Ram and . Ramond, Semiclassical study of quantum scattering on the line, Comm. Math. Phys, vol.177, pp.221-254, 1996.

]. M. Re-si, . Reed-&-b, and . Simon, Methods of modern mathematical physics, 1975.

]. D. Rob1 and . Robert, Autour de l'approximation semi-classique, Progress in Mathematics, vol.68, 1987.

]. D. Rob2 and . Robert, Revivals of wave packets and Bohr-Sommerfeld quantization rules, Adventures in mathematical physics, Contemp. Math, vol.447, pp.219-235, 2007.

]. D. Rob3 and . Robert, Propagation of coherent states in quatum mechanics and application , proc. CIMPA, 2005.

]. R. Robi1 and . Robinnet, Quantum wave packet revivals Physics Reports, Robi2] R. W. ROBINNET, Wave packets revivals and quasirevivals in onedimesionnal power law potentials, pp.1-119, 2000.

J. Sjöstrand, Microlocal analysis for the periodic magnetic Schrödinger equation and related questions, Microlocal analysis and applications (Montecatini Terme, Lect. Notes in Math, 1495.

J. Sjöstrand, Density of states oscillations for magnetic Schr??dinger operators, Math. Sci. Engrg, vol.186, pp.295-345, 1990.
DOI : 10.1016/S0076-5392(08)63387-1

]. B. Sev and . Sevennec, Majoration topologique de la multiplicité du spectre des surfaces, pp.29-35, 1993.

]. T. Sun and . Sunada, Riemannian covering and isospectral manifolds, Ann. of Math, vol.121, pp.169-186, 1985.

]. M. Tay and . Taylor, Noncommutative harmonic analysis, Mathematical Surveys and Monographs, 1986.

]. S. Vun1, . Vu, and . Ngoc, Sur le spectre des systèmes complètement intégrables semiclassiques avec singularités, 1998.

]. S. Vun2, . Vu, and . Ngoc, Formes normales semi-classiques des systèmes complètement intégrables au voisinage d'un point critique de l'application moment Asymptotic analysis, pp.3-4319, 2000.

]. S. Vun3, . Vu, and . Ngoc, Bohr-Sommerfeld conditions for integrable systems with critical manifolds of focus-focus type, Comm. Pure and Applied Math, vol.53, issue.2, pp.143-217, 2000.

]. S. Vun4, . Vu, and . Ngoc, Systèmes intégrables semi-classiques : du local au global, Panoramas et synthèses 22, 2006.

]. J. Wil and . Williamson, On the algebraic problem concerning the normal form of linear dynamical systems, Amer. J. Math, vol.58, issue.1, pp.141-163, 1936.

]. S. Zel and . Zelditch, Spectral determination of analytic bi-axisymmetric plain domains, Geom. And Func. Ana, vol.10, pp.628-677, 2000.