On the infinitesimal geometry of integrable systems. (English) Zbl 1005.37510

Baider, A.; Churchill, R. C.; Rod, D. L.; Singer, M. F.

Shadwick, William F. (ed.) et al., Mechanics days. Proceedings of a workshop, June 12, 1992. Providence, RI: American Mathematical Society. Fields Inst. Commun. 7, 5-56 (1996).

The authors study nonintegrability of Hamiltonian systems giving first a more detailed version of S. L. Ziglin’s theory [Funkts. Anal. Prilozh. 17, No. 1, 8-23 (1983; Zbl 0518.58016)] and present the ideas in the context of linear algebraic groups. They replace the monodromy groups used by Ziglin with differential Galois groups. Finally applications are given.
For the entire collection see [Zbl 0833.00041].

MSC:

37J30	Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria)
12H05	Differential algebra
34M99	Ordinary differential equations in the complex domain
70H07	Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics

Keywords:

nonintegrability of Hamiltonian systems; differential Galois groups

Citations:

Zbl 0518.58016