Kolmogorov–Arnold–Moser theorem

This paper gives a self contained proof of the perturbation theorem for invariant tori in Hamiltonian systems by Kolmogorov, Arnold, and Moser with sharp dieren tiablility hypotheses. The proof follows an idea outlined by Moser in [16] and, as byproducts, gives rise to uniqueness and regularity theorems for invariant tori. 1

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