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Let $Q$ be a closed manifold admitting a locally-free action of a compact Liegroup $G$. In this paper we study the properties of geodesic flows on $Q$ givenby Riemannian metrics which are invariant by such an action. In particular, wewill be interested in the existence of geodesics which are closed up to theaction of some element in the group $G$, since they project to closed magneticgeodesics on the quotient orbifold $Q/G$.

On geodesic flows with symmetries and closed magnetic geodesics on orbifolds