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A new formulation of the generalized Toda lattice equations and their fixed point analysis via the momentum map
Author(s):
Anthony M.
Bloch;
Roger W.
Brockett;
Tudor S.
Ratiu
Journal:
Bull. Amer. Math. Soc.
23
(1990),
477-485.
MSC (1985):
Primary 34A05;
Secondary 22E46
MathSciNet review:
1027895
Retrieve article in:
PDF
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Additional information
References:
- 1.
- M. Adler, On a trace functional for pseudo-differential operators and the symplectic structure of Korteveg-Devries type equations,, Invent. Math. 50 (1979), 219-248. MR 520927
- 2.
- M.F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 16(1982), 1-15. MR 642416
- 3.
- A. M. Bloch, Estimation, principal components and Hamiltonian systems, Systems Control Lett., vol. 6, North-Holland, Amsterdam, 1985, pp. 103-108. MR 801020
- 4.
- A. M. Bloch, Steepest descent, linear programming and Hamiltonian Flows, Contemporary Math, (to appear). MR 1097866
- 5.
- A. M. Bloch, H. Flaschka, and T. Ratiu, A convexity theorem for isospectral sets of Jacobi matrices in a compact Lie algebra, Duke Math. J. (to appear).
- 6.
- A. M. Bloch, R. W. Brockett, and T. Ratiu, Completely integrable gradient flows (to appear). MR 1171760
- 7.
- M. R. Bremner, R. V. Moody, and J. Patera, Tables of dominant weight multiplicities for representations of simple Lie algebras, Marcel Dekker, New York, 1985. MR 779462
- 8.
- R. W. Brockett, Least squares matching problems,, Linear Algebra Appl. 122/123/124 (1989), 761-777. MR 1020010
- 9.
- R. W. Brockett, Dynamical systems that sort lists and solve linear programming problems, Proc. 27th IEEE Conf. on Decision and Control, IEEE, New Jersey, 1988, pp. 799-803.
- 10.
- C. I. Byrnes and J. C. Willems, Least squares estimation, linear programming and momentum, unpublished manuscript, 1984.
- 11.
- M. T. Chu, The generalized Toda lattice, the QR-algorithm and the centre manifold theory, SIAM J. Algebraic Discrete Methods 5 (1984), 187-201. MR 745438
- 12.
- M. W. Davis, Some aspherical manifolds, Duke Math. J. 5 (1987), 105-139. MR 883666
- 13.
- P. Deift, T. Nanda, and C. Tomei, Differential equations for the symmetric eigenvalue problem, SIAM J. Numer. Anal. 20 (1983), 1-22. MR 687364
- 14.
- H. Flaschka, The Toda lattice, Phys. Rev. B(3) 9 (1976), 1924-1925. MR 408647
- 15.
- D. Fried, The cohomology of an isospectral flow, Proc. Amer. Math. Soc. 98 (1986), 363-368. MR 854048
- 16.
- V. Guillemin and S. Sternberg, Convexity properties of the moment mapping, Invent. Math. 67 (1982), 491-513. MR 664117
- 17.
- V. Guillemin and S. Sternberg, On the method of Symes for integrating systems of the Toda type, Lett. Math. Phys. 7 (1983), 113-115. MR 708432
- 18.
- A. Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1956), 620-630. MR 63336
- 19.
- B. Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81 (1959), 973-1032. MR 114875
- 20.
- B. Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. (4) 6 (1973), 413-455. MR 364552
- 21.
- B. Kostant, The solution to a generalized Toda lattice and representation theory, Adv. in Math. 34 (1979), 195-338. MR 550790
- 22.
- B. Kostant, Quantization and representation theory, in Representation theory of Lie groups, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, New York, vol. 34, 1979, pp. 91-150. MR 568880
- 23.
- J. Lagarias, Monotonicity properties of the generalized Toda flow and QR flow, preprint, 1988.
- 24.
- I. G. MacDonald, Algebraic structure of Lie groups, in Representation theory of Lie groups, London Math. Soc. Lecture Note Ser. Cambridge University Press, New York, vol. 34, 1979, pp. 91-150. MR 568880
- 25.
- J. Moser, Finitely many mass points on the line under the influence of an exponential potential, Batelles Recontres, Springer Notes in Physics, Springer-Verlag, Berlin, 1974, pp. 417-497.
- 26.
- W. W. Symes, Hamiltonian group actions and integrable systems, Phys. D 1 (1980), 339-376. MR 601577
- 27.
- W. W. Symes, Systems of Toda type, inverse spectral problems and representation theory, Invent. Math. 59 (1982), 13-51. MR 575079
- 28.
- W. W. Symes, The QR algorithm and scattering for the nonperiodic Toda lattice, Phys. D 4 (1982), 275-280. MR 653781
- 29.
- M. Toda, Studies of a non-linear lattice, Phys. Rep. 8 (1975), 1-125. MR 489137
- 30.
- C. Tomei, The topology of isospectral manifolds of diagonal matrices, Duke Math. J. 51 (1984), 981-996. MR 771391
- 31.
- P. van Moerbeke, The spectrum of Jacobi matrices, Invent. Math. 37 (1976), 45-81. MR 650253
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Additional Information:
DOI:
10.1090/S0273-0979-1990-15960-9
PII:
S 0273-0979(1990)15960-9
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