Paolo Perfetti.
An infinite-dimensional extension of 
a Poincar\'e's result concerning the continuation of periodic orbits.
(84K, tex)

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.