A NEW FORMULATION OF THE GENERALIZED TODA LATTICE EQUATIONS AND THEIR FIXED POINT ANALYSIS VIA THE MOMENTUM MAP

@inproceedings{Bloch2007ANF,
  title={A NEW FORMULATION OF THE GENERALIZED TODA LATTICE EQUATIONS AND THEIR FIXED POINT ANALYSIS VIA THE MOMENTUM MAP},
  author={Anthony M. Bloch and Roger W. Brockett and Tudor S. Ratiu},
  year={2007}
}
The Toda flows are examples of integrable Hamiltonian systems which are of great interest from the point of view of pure mathematics as well as in applications. They originated as a description of a 1-dimensional lattice of particles with exponential interaction [29]. Flaschka [14] found a Lax pair for the equations and Moser [25] analyzed the dynamics and scattering behavior of the system. Adler [1], Kostant [21,22] and Symes [26,27] generalized the results to arbitrary Lie algebras. Symes [28… CONTINUE READING
Highly Cited
This paper has 41 citations. REVIEW CITATIONS

References

Publications referenced by this paper.
Showing 1-10 of 19 references

Finitely many mass points on the line under the influence of an exponential potential, Batelles Recontres

J. Moser
Springer Notes in Physics, Springer-Verlag, Berlin, • 1974
View 4 Excerpts
Highly Influenced

Least squares matching problems

R. W. Brockett
Linear Algebra Appl • 1989
View 2 Excerpts

Monotonicity properties of the generalized Toda flow and QR flow

J. Lagarias
1988
View 1 Excerpt

The cohomology of an isospectral flow

D. Fried
Proc. Amer. Math. Soc • 1986
View 1 Excerpt

Estimation, principal components and Hamiltonian systems, Systems

A. M. Bloch
Control Lett., • 1985
View 1 Excerpt

Tables of dominant weight multiplicities for representations of simple Lie algebras

M. R. Bremner, R. V. Moody, J. Patera
AND TUDOR S. RATIU • 1985
View 1 Excerpt

Least squares estimation, linear programming and momentum, unpublished

C. I. Byrnes, J. C. Willems
1984
View 1 Excerpt

The generalized Toda lattice, the QR-algorithm and the centre manifold theory

M. T. Chu
SIAM J. Algebraic Discrete Methods • 1984
View 1 Excerpt

The topology of isospectral manifolds of diagonal matrices

C. Tomei
Duke Math. J • 1984
View 3 Excerpts