Extended integrability and bi-Hamiltonian systems
The paper deals with the problem of integrability of Hamiltonian systems. The author presents an extension of the Liouville integrability which allows him among other interesting cases, to treat the dynamics of an electron on the torus \(T^2\subset \mathbb{R}^3\) in an electromagnetic field and to prove that the corresponding Hamiltonian system on \(T^*(T^2)\) is bi-Hamiltonian and integrable in an extended sense. The main result consists of the complete classification of all \(\frac{k(k+1)} {2}\) nonequivalent canonical forms of integrable Hamiltonian systems and invariant symplectic structures.
scientific article; zbMATH DE number 1203794