MPEJ Volume 10, No. 3, 37 pp.
Received: Feb 17, 2004. Revised: Feb 26, 2004. Accepted: Mar 1, 2004.

D. Salamon
The Kolmogorov-Arnold-Moser theorem

ABSTRACT: This paper gives a self contained proof of the perturbation theorem 
for invariant tori in Hamiltonian systems by Kolmogorov,
Arnold, and Moser with sharp differentiablility hypotheses. 
The proof follows an idea outlined by Moser in~\cite{M4} and,   
as byproducts, gives rise to uniqueness and regularity 
theorems for invariant tori.\footnote
{The present paper was written in 1986 while I was a postdoc 
at ETH Z\"urich. I didn't publish it at the time because 
the results are well known and the paper is of 
expository nature. The paper is reproduced here with the following
changes:  there are a few updates in the introduction, 
a mistake in Lemma~\ref{le:approx1} and the proof of 
Theorem~\ref{thm:smooth} has been corrected, the 
hypotheses of Theorem~\ref{thm:smooth} have been weakened, and
Lemma~\ref{le:product} has been moved to Section~\ref{sec:smooth}.
The original manuscript can be found on my webpage 
{\bf http://www.math.ethz.ch/~salamon/publications.html}.
}


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