A version of Thirring's approach to the Kolmogorov-Arnold-Moser theorem for quadratic Hamiltonians with degenerate twist

We give a proof of the Kolmogorov-Arnold-Moser (KAM) theorem on the existen ce of invariant tori for weakly perturbed Hamiltonian systems, based on Thi rring's approach for Hamiltonians that are quadratic in the action variable s. The main point of this approach is that the iteration of canonical trans formations on which the proof is based stays within the space of quadratic Hamiltonians. We show that Thirring's proof for nondegenerate Hamiltonians can be adapted to Hamiltonians with degenerate twist. This case, in fact, d rastically simplifies Thirring's proof. (C) 1998 American Institute of Phys ics. [S0022-2488(98)00611-2].