NORMAL FORMS OF SYMMETRICAL HAMILTONIAN-SYSTEMS

[摘要] We study the following question: to what simplest normal form can a Hamiltonian with a symmetry group GAMMA be reduced by a GAMMA-equivariant contactomorphism (a contactomorphism conjugated with each transformation from GAMMA). In particular, we point out conditions under which there exists a GAMMA-equivariant contactomorphism reducing a GAMMA-invariant Hamiltonian to a GAMMA-equivariant Birkhoff normal form. In resonance cases the Birkhoff normal form can be simplified. We present a method of reduction to an invariant normal form, independent of information on symmetries. At the same time under certain conditions the invariant normal form of a GAMMA-invariant Hamiltonian is also GAMMA-invariant and the reduction to it can be realized via a GAMMA-equivariant contactomorphism. We understand the word ''invariant'' in the following sense: two Hamiltonians (GAMMA-invariant) are equivalent (under the action of the group of r-equivariant contactomorphisms) if and only if their invariant normal forms coincide. (C) 1994 Academic Press, Inc.

[发布日期] 1994-07-01