Lie algebraic aspects of the finite nonperiodic Toda flows

Keywords

Toda lattice, Mathematics, Flow (mathematics), Noncommutative geometry, Pure mathematics

References

• Hamiltonian Structure of Non-Abelian Toda LatticeM. Gekhtman — 1998
• Proceedings of the CRM Workshop on Hamiltonian Systems, Transformation Groups and Spectral Transform MethodsSpectral Transform Methods, J. Harnad, Jerrold E. Marsden — 1990
• Lie groups and algebraic groupsÉ. B. Vinberg, A. L. Onishchik, Dimitry Leites — 1990
• A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebraAnthony M. Bloch, H. Flaschka, Tudor S. Raţiu — 1990
• Lie algebras, geometry and Toda-type systemsA. V. Razumov, M. V. Saveliev — 1997
• Hamiltonian methods in the theory of solitonsL. D. Faddeev, Leon A. Takhtajan — 1987
• Convexity properties of the moment mapping. IIVictor Guillemin, S. Sternberg — 1982
• The Toda flow on a generic orbit is integrablePercy Deift, L. C. Li, T. Nanda — 1984
• Peakons, r-matrix and Toda latticeO. Ragnisco, M. Bruschi — 1996
• A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulusAnthony M. Bloch, H. Flaschka, Tudor S. Raţiu — 1993
• The spectrum of Jacobi matricesPierre van Moerbeke — 1976
• Integrable Hamiltonian systems connected with graded Lie algebrasA. G. Reiman — 1982
• Group-Theoretical Methods for Integration of Nonlinear Dynamical SystemsA. N. Leznov, M. V. Saveliev — 1992
• Some aspherical manifoldsMichael W. Davis — 1987
• The solution to a generalized Toda lattice and representation theoryBertram Kostant — 1979
• The topology of isospectral manifolds of tridiagonal matricesCarlos Tomei — 1984
• Maximally non-abelian Toda systems☆A.V. Razumov, M.V. Saveliev — 1996
• Faces of Relativistic Toda ChainS. Kharchev, А. Миронов, Alexei Zhedanov — 1997
• Classical and quantum-mechanical systems of Toda lattice type. IRoe Goodman, Nolan R. Wallach — 1982
• A new formulation of the generalized Toda lattice equations and their fixed point analysis via the momentum mapAnthony M. Bloch, Roger W. Brockett, Tudor S. Raţiu — 1990

Cited by

• The Finite Non-periodic Toda Lattice: A Geometric and Topological ViewpointYuji Kodama, Barbara A. Shipman — 2008
• New method for constructing semi-invariants and integrals of the full symmetric sl_n Toda latticeA. S. Sorin, Yu. B. Chernyakov — 2015
• Explicit Semi-invariants and Integrals of the Full Symmetric sl_nsln Toda LatticeYu. B. Chernyakov, A. S. Sorin — 2013
• Networks of Hamiltonian systems and feedbackMohamed-Ali Belabbas — 2009
• Multi‐Hamiltonian structure for the finite defocusing Ablowitz‐Ladik equationMichael Gekhtman, Irina Nenciu — 2007
• Explicit Construction of First Integrals for the Toda Flow on a Classical Simple Lie AlgebraPatrick Seegmiller — 2015
• Full symmetric Toda system and vector fields on the group S O</mYu. B. Chernyakov, G. Sharygin — 2025

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