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Colin de Verdière, Yves

Quasi-modes sur les variétés Riemanniennes. (French) Zbl 0449.53040

Invent. Math. 43, 15-52 (1977).
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Cited in 1 Review
Cited in 44 Documents

MSC:

53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions

Keywords:

Laplacian; geodesic flow; periodic geodesics

Citations:

Zbl 0307.35071; Zbl 0281.53036; Zbl 0255.35074; Zbl 0175.203
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\textit{Y. Colin de Verdière}, Invent. Math. 43, 15--52 (1977; Zbl 0449.53040)
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References:

[1] A1 Arnold, V.I.: Modes and quasi-modes. Functional Analysis and its applications6, 94-101 (1972) · Zbl 0251.70012
[2] AA Arnold, V.I., Avez, A.: Ergodic problems of classical mechanics. New-York-Amsterdam: Benjamin 1967
[3] A2 Arnold, V.I.: On a caracteristic class entering in the quantization conditions. Functional Analysis and its applications1, 1-13 (1967)
[4] BGM Berger, M., Gauduchon, P., Mazet, E.: Le spectre d’une variété riemannienne. Lectures Notes 194. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0223.53034
[5] CA Cassels, J.W.S.: An Introduction to diophantine approximation. Cambridge: Cambridge University Press 1965
[6] CV Colin de Verdiere, Y.: Spectre du laplacien et longueurs des géodésiques fermées II. Compositio mathematica,27, 159-184 (1973)
[7] D Duistermaat, J.J.: Oscillatory integrals, Lagrange immersions, and unfolding of singularities. Comm. Pure and Appl. Math.,27, 207-281 (1974) · Zbl 0285.35010
[8] D.G Duistermaat, J.J., Guillemin, V.: The spectrum of positiv elliptic operators and periodic geodesics. Invent. Math.29, 39-79 (1975) · Zbl 0307.35071
[9] D.H. Duistermaat, J.J., Hörmander, L.: Fourier integral operators II. Acta Math.128, 183-269 (1972) · Zbl 0232.47055
[10] G Guillemin, V.: Symplectic Spinors and partial differential equations. Colloque international de géométrie symplectique et physique mathématique. Aix (Juin 1974), C.N.R.S.
[11] H1 Hörmander, L.: Fourier integral operators I. Acta Math.127, 79-183 (1971) · Zbl 0212.46601
[12] H2 Hörmander, L.: The spectral function of an elliptic operator. Acta Math.121, 193-218 (1968) · Zbl 0164.13201
[13] K Klingenberg, W.: Der Indexsatz für geschlossene Geodätische. Math. Zeit.139, 231-256 (1974) · Zbl 0306.58009
[14] L1 Lazutkin, V.F.: The existence of caustics for a billiard problem in a convex domain. Math. USSR Izvestija7, 185-214 (1973) · Zbl 0277.52002
[15] L2 Lazutkin, V.F.: Asymptotics of the eigenvalues of the laplacian and quasi-modes ... Math. USSR Izvestija7, 439-466 (1973) · Zbl 0282.35063
[16] RL Randol, B.: A lattice-point problem. Trans. Amer. Math. Soc.121, 257-268 (1966) · Zbl 0135.10601
[17] R Ralston, J.V.: Construction of approximate eigenfunctions ... Preprint (1975)
[18] S Moser, J.K., Siegel, C.L.: Lectures on Celestial mechanics. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0312.70017
[19] SU Souriau, J.M.: Indice de Maslov des variétés lagrangiennes orientables, comptes-rendus de l’Académie des sciences de Paris276A, 1025-1026 (1973) · Zbl 0254.58007
[20] V Voros, A.: The WKB-method for non-separable systems. Colloque international de géométrie symplectique et physique mathématique. Aix (Juin 1974), C.N.R.S.
[21] V de C van der Corput, J.G.: Over roosterpunten in het platte vlak. Groningen: Noordhoff 1919 · JFM 47.0158.02
[22] W1 Weinstein, A.: Fourier integral operators, quantization and the spectra of riemannian manifold; colloque international de géométrie symplectique et physique mathématique. Aix (Juin 1974), C.N.R.S.
[23] W2 Weinstein, A.: Symplectic manifolds and their lagrangian submanifolds. Advances in Math.6, 329-346 (1971) · Zbl 0213.48203
[24] B.L Babich, Lazutkin, V.F.: On eigenfunctions concentrated at a closed geodesic; problems in Math. Phys. N 2, Leningrad Unversity, 1967
[25] B. Babich: On eigenfunctions concentrated at a closed geodesic; Zapiski Nauchnyck Seminarov Lomi, N 9, Leningrad (1968) (Englisch translation: Math. Problems in Wawe propagation theory, Consultant Bureau, New York-London, 1970)
[26] B.B. Babich, Bouldyrev: Asymptotical methods in the theory of short waves deffractions. Moscow Nauka (1972)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.