Paolo Perfetti
Hamiltonian equations on ${\Bbb T}^\infty$} and almost-periodic solutions
(906K, ps)
ABSTRACT. {{\bf Abstract} A class of ordinary differential equations
exhibiting almost-periodic
solutions is studied. The equations are canonical
and the hamilton functions are of the type {\it
kinetic energy + potential energy}. The potential-energy 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 $\vert i\vert\to\infty$) }