Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics (Q2684513)

The authors of the paper considered \(M\) be a compact simply connected manifold satisfying \(H^{*}(M; Q)\cong T_{d,n+1}(x)\) for integers \(d\geq 2\) and \(n\geq 1\). Further if all prime closed geodesics on \((M,F)\) with an irreversible bumpy Finsler metric \(F\) are elliptic, then either there exist exactly \(dn(n+1)/2\) (when \(d\geq 2\) is even) or \((d+1)\) (when \(d\geq 3\) is odd) distinct closed geodesics, or there exist infinitely many distinct closed geodesics. Results obtained by them are very interesting.