96-473 Paolo Perfetti.
An infinite-dimensional extension of a Poincar\'e's result concerning the continuation of periodic orbits. (84K, tex) Oct 4, 96
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Abstract. We study the existence of periodic solutions for the infinite-dimensional second order system $\ddot x=V_{x},\ x\in{\bf T}^{{\bf Z}_+}.$ Using the Implicit-Function-Theorem we prove the existence of time-periodic solutions at \lq\lq high frequencies"; no \lq\lq smallness condition" on $V(x)$ is required.

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