98-121 Chandre C., Jauslin H.R.

Twistless Version of Thirring's Approach to the KAM Theorem for Quadratic Hamiltonians (35K, RevTex) Mar 4, 98

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Abstract. We give a proof of the KAM theorem on the existence of invariant tori for weakly perturbed Hamiltonian systems, based on Thirring's approach for Hamiltonians that are quadratic in the action variables. The main point of this approach is that the iteration of canonical transformations 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 twistless Hamiltonians. This twistless assumption, in fact, drastically simplifies Thirring's proof.

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