Isospectral deformations of random Jacobi operators
type: Item
instance of: scholarly article
title: Isospectral deformations of random Jacobi operators
zbMATH Open document ID: 0768.58038
DOI: 10.1007/BF02096774
author: O. Knill
published in: Communications in Mathematical Physics
publication date: 1993-05-16T00:00:00Z
review text: Defining a dynamical system as an automorphism of the probability space, the author establishes the integrability of infinite dimensional Hamiltonian systems obtained by making isospectral deformations of random Jacobi operators. The author shows also that time 1 map of such a so- called random Toda flow can be expressed by a \(QR\) decomposition (that is, as a product of two matrices \(Q\) and \(R\) where \(Q\) is orthogonal and \(R\) is upper triangular). A number of questions are raised which fellow research workers will find interesting.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 70H20
zbMATH DE Number: 165690
zbMATH Keywords: Toda flows
zbMATH Keywords: dynamical systems
zbMATH Keywords: Jacobi operators
reviewed by: Chandra Shekhar Sharma
MaRDI profile type: Publication
cites work: The integration of semi-infinite Toda chain by means of inverse spectral problem
cites work: Integration of some chains of nonlinear difference equations by the method of the inverse spectral problem
cites work: On the Global Convergence of the Toda Lattice for Real Normal Matrices and Its Applications to the Eigenvalue Problem
cites work: The Generalized Toda Flow, the QR Algorithm and the Center Manifold Theory
cites work: A differential equation approach to the singular value decomposition of bidiagonal matrices
cites work: Inverse spectral theory for random Jacobi matrices
cites work: Q3997506
cites work: The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics
cites work: Nonlinear wave equations and constrained harmonic motion
cites work: Toda flows with infinitely many variables
cites work: Matrix factorizations and integrable systems
cites work: Ordinary Differential Equations and the Symmetric Eigenvalue Problem
cites work: Generalized affine lie algebras and the solution of a class of flows associated with the QR eigenvalue algorithm
cites work: The rotation number for finite difference operators and its properties
cites work: On the Toda Lattice. II: Inverse-Scattering Solution
cites work: Hyperbolic sets for twist maps
cites work: The rotation number for almost periodic potentials
cites work: A complete solution of the periodic Toda problem
cites work: Periodic orbits for reversible, symplectic mappings
cites work: The solution to a generalized Toda lattice and representation theory
cites work: Stochastic Schrödinger operators and Jacobi matrices on the strip
cites work: Long time behaviour of an infinite particle system
cites work: Q5552090
cites work: Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
cites work: Amount of rotation about a point and the Morse index
cites work: Q3895938
cites work: The spectrum of Jacobi matrices
cites work: Q3915684
cites work: Three integrable Hamiltonian systems connected with isospectral deformations
cites work: Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
cites work: Q4692312
cites work: Kotani theory for one dimensional stochastic Jacobi matrices
cites work: The QR algorithm and scattering for the finite nonperiodic Toda lattice
cites work: Systems of Toda type, inverse spectral problems, and representation theory
cites work: Theory of nonlinear lattices
cites work: Invariant families of cones and Lyapunov exponents
description: scientific article; zbMATH DE number 165690