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We show that for a generic Riemannian or reversible Finsler metric on acompact differentiable manifold $M$ of dimension at least three all closedgeodesics are simple and do not intersect each other. Using results byContreras~\cite{C2010} \cite{C2011} this shows that for a generic Riemannianmetric on a compact and simply-connected manifold all closed geodesics aresimple and the number $N(t)$ of geometrically distinct closed geodesics oflength $\le t$ grows exponentially.

Simple closed geodesics in dimensions $\ge 3$