The Toda lattice is super-integrable
arXiv:math-ph/0507051 · doi:10.1016/j.physa.2006.01.001
Abstract
We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient of the proof is the use of some special action--angle coordinates introduced by Moser to solve the equations of motion.
arXiv comment8 pages
References in corpus (1)
Cited by in corpus (15)
- Classical and Quantum Superintegrability with Applications
- Hidden Symmetries of Dynamics in Classical and Quantum Physics
- Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
- A maximally superintegrable system on an n-dimensional space of nonconstant curvature
- On maximally superintegrable systems
- Smooth and Peaked Solitons of the CH equation
- Generalised Eisenhart lift of the Toda chain
- A nonseparable quantum superintegrable system in 2D real Euclidean space
- An Algebraic Geometric Foundation for a Classification of Superintegrable Systems in Arbitrary Dimension
- An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
- Exterior dissipation, proportional decay, and integrals of motion
- Linearizing Toda and SVD flows on large phase spaces of matrices with real spectrum
- A note on the superintegrability of the Toda lattice
- Near integrability of kink lattice with higher order interactions
- Discrete-time maximally superintegrable systems and deformed symmetry algebras: the Calogero-Moser case