×

zbMATH — the first resource for mathematics

The spectrum of Jacobi matrices. (English) Zbl 0361.15010

MSC:
37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
14K99 Abelian varieties and schemes
15B57 Hermitian, skew-Hermitian, and related matrices
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Akhiezer, N. I.: The classical moment problem. Edinburgh. Oliver and Boyd 1965 · Zbl 0135.33803
[2] Flaschka, H.: The Toda lattice I. Phys. Rev., Sect. B9, 1924-1925 (1974) · Zbl 0942.37504
[3] Flaschka, H.: The Toda lattice II. Progr. Theor. Phys.51, 703-716 (1974) · Zbl 0942.37505
[4] Gantmacher, F. R., Krein, M. G.: Oszillationsmatrizen, Oszillation Kerne und kleine Schwingungen mechanischer Systeme. Berlin: Akad. Verlag 1960 · Zbl 0088.25103
[5] Goldstein, H.: Classical mechanics. Reading: Addison Wesley 1959 · Zbl 0043.18001
[6] Jacobi, C. G. L.: Gesammelte Werke. Bd. 7 supplement: Vorlesungen über Dynamik. Clebsch, A., Reimer, G. (Hrsg.). Berlin: Reimer 1884 (see 26, and 30. Vorlesung)
[7] Kac, M., van Moerbeke, P.: On some periodic Toda lattice. Proc. Nat. Acad. Sci. USA72(4), 1627-1629 (1975) · Zbl 0343.34003
[8] Kac, M., van Moerbeke, P.: The solution of the periodic Toda lattice. Proc. Nat. Acad. Sci., USA72(8), 2879-2880 (1975) · Zbl 0343.34004
[9] Lax, P. D.: Integrals of non-linear equations of evolution and solitary waves. Comm. Pure. Appl. Math.21, 467-490 (1968) · Zbl 0162.41103
[10] McKean, H. P., van Moerbeke, P.: The spectrum of Hill’s equation, Inventiones math.30, 217-274 (1975) · Zbl 0319.34024
[11] Moser, J.: Finitely many mass points on the line under the influence of an exponential potential?An integrable system. Battelle Rencontres summer lectures. Lecture Notes in Math. · Zbl 0323.70012
[12] Toda, M.: Wave propagation in anharmonic lattices. J. of Phys. Soc. of Japan23, 501-506(1967)
[13] Whittaker, E. T.: A treatise on the analytical dynamics of particles and rigid bodies. New York: Dover 1904 · JFM 35.0682.01
[14] Flaschka, H., McLaughlin, D. W.: Canonically conjugate variables for the Korteweg-de Vries equation and the Toda Lattice. Preprint · Zbl 1109.35374
[15] Manakov, S. V.: Integration of discrete dynamical systems. Zhurnal Teor. Exp. Fiz.67, 543 (1974)
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.