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

Abstract

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 $C_{2 \pi}([0,2\pi],\Omega) \times (0,+ \infty)$. As the main topological tool we apply the degree for equivariant gradient maps.