  The goal of this article is to study closed connected sets of periodic
solutions, of autonomous second order Hamiltonian systems, emanating from
infinity. The main idea is to apply the degree for SO(2)-equivariant gradient
operators defined by the second author. Using the results due to Rabier we show
that we cannot apply the Leray-Schauder degree to prove the main results of
this article. It is worth pointing out that since we study connected sets of
solutions, we also cannot use the Conley index technique and the Morse theory.
