A new formulation of the generalized Toda lattice equations and their fixed point analysis via the momentum map

DOI10.1090/S0273-0979-1990-15960-9zbMath0715.58033OpenAlexW2008201725MaRDI QIDQ3202879

Roger W. Brockett, Anthony M. Bloch, Tudor S. Ratiu

Publication date: 1990

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1990-15960-9

zbMATH Keywords

momentum mapToda lattice equationToda flow

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamics induced by flows and semiflows (37C10) Lie groups (22E99)

Related Items

Hessenberg varieties, Slodowy slices, and integrable systems, Scaled Toda-like flows, Multi-component hierarchies of double bracket equations., Algebraic analysis of a discrete hierarchy of double bracket equations, Hamiltonian structure of dynamical systems which solve linear programming problems, A new nonlinear dynamical system that leads to eigenvalues, Singular-value decomposition via gradient and self-equivalent flows, Numerical solution of isospectral flows, Completely integrable gradient flows, A Lie bracket decomposition and its application to flows on symmetric matrices, The geometric nature of the Flaschka transformation, A differential equation for diagonalizing complex semisimple Lie algebra elements, Bruhat order in full symmetric Toda system, Algebraic aspects of Brockett type equations, A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebra, Isospectral flows on symmetric matrices and the Riccati equation, Toda flows, inverse spectral transform and realization theory

Cites Work

• Unnamed Item
• Unnamed Item
• A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebra
• The topology of isospectral manifolds of tridiagonal matrices
• Hamiltonian group actions and integrable systems
• The QR algorithm and scattering for the finite nonperiodic Toda lattice
• On the method of Symes for integrating systems of the Toda type
• Estimation, principal components and Hamiltonian systems
• Some aspherical manifolds
• Least squares matching problems
• The solution to a generalized Toda lattice and representation theory
• Systems of Toda type, inverse spectral problems, and representation theory
• Convexity properties of the moment mapping
• Completely integrable gradient flows
• The spectrum of Jacobi matrices
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Ordinary Differential Equations and the Symmetric Eigenvalue Problem
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• The Generalized Toda Flow, the QR Algorithm and the Center Manifold Theory
• Convexity and Commuting Hamiltonians
• On convexity, the Weyl group and the Iwasawa decomposition
• The Toda lattice. II. Existence of integrals
• The Cohomology of an Isospectral Flow
• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix