Periodic solutions of autonomous $S^1$-symmetric Newtonian systems

The aim of this paper is to formulate necessary conditions and sufficient ones for the existence of closed connected sets of nonstationary $2\pi$-periodic solutions of $S^1$-symmetric Newtonian systems in $C_{2\pi }([0,2\pi ],\mathrm{\Omega })\times (0,+\mathrm{\infty })$. As the main topological tool we apply the degree for equivariant gradient maps.