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.