Abstract
The asymptotic behavior of the eigenfunctions for the triaxial ellipsoid
has been studied in the papers .of V. P. Bykov [1] and L. A. Vainshtein [2].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literature Cited
Vainshtein, L. A., Radiation flux in the triaxial ellipsoid, in High-Power Electronics [in Russian], Vol. 4, Nauka, Moscow (1965), pp. 93–106.
Bykov, V. P., The geometrical optics of three-dimensional vibrations in open resonators, in: High-Power Electronics [in Russian], Vol. 4, Nauka, Moscow (1965), pp. 66–93.
Leontovich, M. A., On the method of solving problems concerning the propagation of waves along the surface of the earth, Izv. Akad. Nauk SSSR, ser. fiz., Vol. B, No. 16 (1944).
Fok, V. A., The field of a plane wave near the surface of a conducting body, Izv. Akad. Nauk SSSR, ser. fiz., Vol. 10, No. 2, pp, 171–186 (1946),
Buldyrev, V. S., The short wave asymptotic behavior of the eigenfunctions of the Helmholtz operator, Dokl. Akad. Nauk SSSR, 163, No. 4, pp. 853–856 (1965).
Babich, V. M., and Lazutkin, V. F., Eigenfunctions concentrated near a closed geodesic, in: Topics in Mathematical Physics, Vol. 2, M. Sh. Birman, ed.; Consultants Bureau, New York (1968).
Alekseev, A. S., Babich, V. M., and Fel’chinskii, V. Ya., The ray method for computing the intensity of wave fronts, in: Problems in the Dynamical Theory of Propagation of Seismic Waves [in Russian], Len. Gos. Univ., No. 5, pp. 3–35 (1961).
Rashevskii, P. K., Riemannian Geometry and Tensor Analysis [in Russian], Mir, Moscow (1967).
Bishop, R. L., and Crittenden, R. J., Geometry of Manifolds, Academic Press, New York (1964).
Milnor, J., Morse Theory, Princeton Univ. Press, Princeton (1963).
Smirnov, V. I., A Course in Higher Mathematics [in Russian], Moscow (1949).
Bourbaki, N., Functions of a Real Variable, Elementary Theory [Russian translation], Nauka, Moscow (1965).
Segal, I. E., Foundations of the theory of dynamical systems of infinitely many degrees of freedom, II, Canadian J. Math., Vol. 13, No. 1, (1961).
Chernikov, P. A., A system with Hamiltonian in the form of a time-dependent quadratic form of p and q,, Zh. Éksp. Teor. Fiz., Vol. 53, No. 3, pp. 1006–1017 (1967).
Editor information
Rights and permissions
Copyright information
© 1970 Consultants Bureau, New York
About this chapter
Cite this chapter
Babich, V.M. (1970). Eigenfunctions Concentrated in a Neighborhood of a Closed Geodesic. In: Babich, V.M. (eds) Mathematical Problems in Wave Propagation Theory. Seminars in Mathematics, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0334-4_2
Download citation
DOI: https://doi.org/10.1007/978-1-4757-0334-4_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-0336-8
Online ISBN: 978-1-4757-0334-4
eBook Packages: Springer Book Archive