 93171 Chierchia Luigi, Falcolini Corrado
 A Direct Proof of a Theorem by Kolmogorov in Hamiltonian Systems
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Jun 8, 93

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Abstract. \begin{abstract}
\nin
We present a direct proof of Kolmogorov's theorem on the persistence of
quasiperiodic solutions for nearly integrable, realanalytic
Hamiltonian systems with Hamiltonians of the form
$\frac{1}{2} y\cdot y\e f(x)$ where $(y,x)$ $\in$ $\rN \times\tN$
are standard symplectic coordinates.
The method of proof consists in constructing, via graph theory,
the formal solution as a formal power series in $\e$
and to show that the $k^{\rm th}$ coefficient of
such formal series can be bounded by a constant to the $k^{th}$
power. All details are presented in a self contained way (included what is
needed from the theory of graphs).
\end{abstract}
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