Arnol’d, V. I. Modes and quasimodes. (English. Russian original) Zbl 0251.70012 Funct. Anal. Appl. 6, 94-101 (1972); translation from Funkts. Anal. Prilozh. 6, No. 2, 12-20 (1972). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 ReviewsCited in 47 Documents MSC: 70J10 Modal analysis in linear vibration theory 74K15 Membranes 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation × Cite Format Result Cite Review PDF Full Text: DOI References: [1] R. Perrin, Selection rules for the splitting of degenerate pairs of natural frequencies of thin circular rings, Acustica,25, No. 2, 69-72 (1971). [2] R. Thom and H. Levine, Singularities of Differentiable Mappings [Russian translation], Mir, Moscow (1968). [3] L. D. Landau and E. M. Lifshitz, Quantum Mechanics. Non-relativistic Theory, Addison-Wesley (1958). · Zbl 0081.22207 [4] V. I. Arnol’d, Singularities of smooth mappings, Uspekhi Matem. Nauk,23, No. 1, 3-44 (1968). [5] R. Thom, Les symetries brisees en physique macroscopique et la mécanique quantique, Publ. IHES (1970). [6] J. B. Keller and S. I. Rubinow, Asymptotic solution of eigenvalue problems, Ann. Phys.,9, No. 1, 24-75 (1960). · Zbl 0087.43002 · doi:10.1016/0003-4916(60)90061-0 [7] A. I. Baz?, Ya. B. Zel’dovich, and A. M. Perelomov, Scattering, Reactions and Decay in Nonrelativistic Quantum Mechanics, Nauka, Moscow (1971). English translation, Israel Program for Scientific Translations, Ltd., Jerusalem (1969). [8] V. M. Babich, V. S. Buldyrev, and V. F. Lazutkin, Application of the methods of mathematical diffraction theory to the problem of the asymptotics of the characteristic numbers and functions of Laplace operators, Partial Differential Equations, Sibirsk. Otdel., Akad. Nauk SSSR, Moscow (1970). [9] V. P. Bykov and L. A. Vainshtein, High Power Electronics,4, Nauka, Moscow (1965). 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.