Isospectral deformations of random Jacobi operators

DOI10.1007/BF02096774zbMath0768.58038MaRDI QIDQ1208032

Oliver Knill

Publication date: 16 May 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

dynamical systemsJacobi operatorsToda flows

Mathematics Subject Classification ID

Other physical applications of random processes (60K40) Hamilton-Jacobi equations in mechanics (70H20) Dynamical systems with hyperbolic behavior (37D99)

Related Items

Renormalization of random Jacobi operators, Topological entropy of standard type monotone twist maps, Ergodic Jacobi matrices and conformal maps, Factorization of random Jacobi operators and Bäcklund transformations, Billiards in the \(l^p\) unit balls of the plane.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The rotation number for finite difference operators and its properties
• Amount of rotation about a point and the Morse index
• Kotani theory for one dimensional stochastic Jacobi matrices
• The QR algorithm and scattering for the finite nonperiodic Toda lattice
• A differential equation approach to the singular value decomposition of bidiagonal matrices
• Integration of some chains of nonlinear difference equations by the method of the inverse spectral problem
• Long time behaviour of an infinite particle system
• The integration of semi-infinite Toda chain by means of inverse spectral problem
• Stochastic Schrödinger operators and Jacobi matrices on the strip
• Periodic orbits for reversible, symplectic mappings
• The solution to a generalized Toda lattice and representation theory
• Theory of nonlinear lattices
• Systems of Toda type, inverse spectral problems, and representation theory
• The rotation number for almost periodic potentials
• Three integrable Hamiltonian systems connected with isospectral deformations
• The spectrum of Jacobi matrices
• Toda flows with infinitely many variables
• Inverse spectral theory for random Jacobi matrices
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• Matrix factorizations and integrable systems
• Ordinary Differential Equations and the Symmetric Eigenvalue Problem
• The Generalized Toda Flow, the QR Algorithm and the Center Manifold Theory
• On the Global Convergence of the Toda Lattice for Real Normal Matrices and Its Applications to the Eigenvalue Problem
• Hyperbolic sets for twist maps
• Invariant families of cones and Lyapunov exponents
• The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• A complete solution of the periodic Toda problem
• On the Toda Lattice. II: Inverse-Scattering Solution
• Generalized affine lie algebras and the solution of a class of flows associated with the QR eigenvalue algorithm
• Nonlinear wave equations and constrained harmonic motion