A system is integrable if the Liouville integrability condition holds or the Hamilton-Jacobi equation is completely separable.
The problem is, are the two the same actually? Namely, the one is implied by the other?
A system is integrable if the Liouville integrability condition holds or the Hamilton-Jacobi equation is completely separable.
The problem is, are the two the same actually? Namely, the one is implied by the other?