00-85 Paolo Perfetti

Hamiltonian equations on ${\Bbb T}^\infty$} and almost-periodic solutions (906K, ps) Feb 23, 00

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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 $\vert i\vert\to\infty$) }

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