Babelon, Olivier (ed.) et al., Integrable systems: the Verdier memorial conference. Actes du colloque international de Luminy, France, July 1-5, 1991. Boston, MA: Birkhäuser. Prog. Math. 115, 239-249 (1993).
A system of differential equations is called bi-Hamiltonian if it can be written in Hamiltonian form in two distinct ways: $dx/dt = J\sb 1\nabla H\sb 1= J\sb 2\nabla H\sb 0$. The bi-Hamiltonian structure determined by $J\sb 1$, $J\sb 2$, is compatible if the sum $J\sb 2+ J\sb 2$ is also Hamiltonian. The bi-Hamiltonian structure is nondegenerate if the operator $J\sb 1$ is nonsingular.
First the author reviews some results on the canonical forms for compatible, nondegenerate complex-analytic bi-Hamiltonian systems. Secondly, the author briefly describes the results of Brouzet and Fernandes on integrable Hamiltonian systems without bi-Hamiltonian structures. For the entire collection see [Zbl 0807.00017
|37J35||Completely integrable systems, topological structure of phase space, integration methods|
|37K10||Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies|