Toda Lattice
Total energy H:–
Momentum P:–
I₂ (2nd integral):–
I₃ (3rd integral):–
dH/H₀:–
Toda lattice (1967): V(r) = e^(-r) + r
H = Σpᵢ²/2 + Σe^(qᵢ₊₁-qᵢ)
Flaschka variables:
aₙ = ½e^(-(qₙ₊₁-qₙ)/2)
bₙ = -pₙ/2
Isospectral flow: dL/dt = [B,L]
Lax pair → N conserved Iₖ = tr(Lᵏ)
Arnold-Liouville: compact level sets = tori, action-angle variables exist.
H = Σpᵢ²/2 + Σe^(qᵢ₊₁-qᵢ)
Flaschka variables:
aₙ = ½e^(-(qₙ₊₁-qₙ)/2)
bₙ = -pₙ/2
Isospectral flow: dL/dt = [B,L]
Lax pair → N conserved Iₖ = tr(Lᵏ)
Arnold-Liouville: compact level sets = tori, action-angle variables exist.