 0085 Paolo Perfetti
 Hamiltonian equations on ${\Bbb T}^\infty$} and almostperiodic solutions
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Feb 23, 00

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Abstract. {{\bf Abstract} A class of ordinary differential equations
exhibiting almostperiodic
solutions is studied. The equations are canonical
and the hamilton functions are of the type {\it
kinetic energy + potential energy}. The potentialenergy part is a
multiperiodic function of infinite angles and
we find solutions $(A_i(t),\vaerphi_i(t))$ $A_i\in{\Bbb R},$
$\varphi_i\in{\Bbb T},$ $i\in{\Bbb Z}^d$ that are continuations of
$(A_i^o,\varphi^o_i+\omega_it), t\in{\Bbb R}$
i.e. the solutions when the potential energy is absent.
The proof is based on the extension to infinite
variables of the KAM theorem in the \lq\lq configurational version"
and the kinetic energy is needed unbounded ($\vert \omega_i\vert\to
+\infty$ as $\vert i\vert\to\infty$) }
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