Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case. (English) Zbl 0702.58024

Eliasson, L. H.

Comment. Math. Helv. 65, No. 1, 4-35 (1990).

The problem of normal forms of Hamiltonian systems near an elliptic stationary point is considered. More concretely, the case when the Hamiltonian system has several integrals which commute for the Poisson bracket is treated as well as the case of an integrable system. Relations with some other structures are clarified and generalized, e.g. the hyperbolic one. Many illustrating examples are given.

Reviewer: J.Andres

MSC:

37J99

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Keywords:

Cartan subalgebras; normal forms of Hamiltonian systems