Closed geodesics on connected sums and $3$-manifolds

We study the asymptotics of number $N(t)$ geometrically distinct closed geodesics length $\leq t$ a Riemannian or Finsler metric on connected sum two compact manifolds dimension at least three with non-trivial fundamental groups, and apply results to prime decomposition three-manifold. In particular we show that function grows like numbers $3$-manifold infinite group. It follows generic has infinitely many geodesics. also consider case manifold positive first Betti simplyconnected which is not homeomorphic sphere.